results for au:Serone_M in:hep-th

- May 16 2018 hep-th cond-mat.stat-mech arXiv:1805.05882v1Perturbation theory of a large class of scalar field theories in $d<4$ can be shown to be Borel resummable using arguments based on Lefschetz thimbles. As an example we study in detail the $\lambda \phi^4$ theory in two dimensions in the $Z_2$ symmetric phase. We extend the results for the perturbative expansion of several quantities up to N$^8$LO and show how the behavior of the theory at strong coupling can be recovered successfully using known resummation techniques. In particular, we compute the vacuum energy and the mass gap for values of the coupling up to the critical point, where the theory becomes gapless and lies in the same universality class of the 2d Ising model. Several properties of the critical point are determined and agree with known exact expressions. The results are in very good agreement (and with comparable precision) with those obtained by other non-perturbative approaches, such as lattice simulations and Hamiltonian truncation methods.
- We study quantum mechanical systems with a discrete spectrum. We show that the asymptotic series associated to certain paths of steepest-descent (Lefschetz thimbles) are Borel resummable to the full result. Using a geometrical approach based on the Picard-Lefschetz theory we characterize the conditions under which perturbative expansions lead to exact results. Even when such conditions are not met, we explain how to define a different perturbative expansion that reproduces the full answer without the need of transseries, i.e. non-perturbative effects, such as real (or complex) instantons. Applications to several quantum mechanical systems are presented.
- In quantum mechanics and quantum field theory perturbation theory generically requires the inclusion of extra contributions non-perturbative in the coupling, such as instantons, to reproduce exact results. We show how full non-perturbative results can be encoded in a suitable modified perturbative series in a class of quantum mechanical problems. We illustrate this explicitly in examples which are known to contain non-perturbative effects, such as the (supersymmetric) double-well potential, the pure anharmonic oscillator, and the perturbative expansion around a false vacuum.
- Jun 10 2016 hep-th cond-mat.stat-mech arXiv:1606.02771v2We study the numerical bounds obtained using a conformal-bootstrap method - advocated in ref. [1] but never implemented so far - where different points in the plane of conformal cross ratios $z$ and $\bar z$ are sampled. In contrast to the most used method based on derivatives evaluated at the symmetric point $z=\bar z =1/2$, we can consistently "integrate out" higher-dimensional operators and get a reduced simpler, and faster to solve, set of bootstrap equations. We test this "effective" bootstrap by studying the 3D Ising and $O(n)$ vector models and bounds on generic 4D CFTs, for which extensive results are already available in the literature. We also determine the scaling dimensions of certain scalar operators in the $O(n)$ vector models, with $n=2,3,4$, which have not yet been computed using bootstrap techniques.
- Jan 21 2016 hep-th arXiv:1601.05325v2We compute in closed analytical form the minimal set of "seed" conformal blocks associated to the exchange of generic mixed symmetry spinor/tensor operators in an arbitrary representation (l,\bar l) of the Lorentz group in four dimensional conformal field theories. These blocks arise from 4-point functions involving two scalars, one (0,|l-\bar l|) and one (|l-\bar l|,0) spinors or tensors. We directly solve the set of Casimir equations, that can elegantly be written in a compact form for any (l,\bar l), by using an educated ansatz and reducing the problem to an algebraic linear system. Various details on the form of the ansatz have been deduced by using the so called shadow formalism. The complexity of the conformal blocks depends on the value of p=|l-\bar l | and grows with p, in analogy to what happens to scalar conformal blocks in d even space-time dimensions as d increases. These results open the way to bootstrap 4-point functions involving arbitrary spinor/tensor operators in four dimensional conformal field theories.
- Oct 08 2015 hep-th astro-ph.CO arXiv:1510.01969v2We study how the coupling with gravity of theories with non-linearly realized space-time symmetries is modified when one changes the parametrization of the coset. As an example, we focus on the so-called Galileon duality: a reparametrization which maps a Galilean invariant action into another one which enjoys the same symmetry. Starting with a standard coupling with gravity, with a parametric separation between the Planck scale and the typical scale of the coset, one ends up with a theory without such a separation. In particular an infinite set of higher-dimension operators are relevant when the superluminality of the Galileon is measurable in the effective theory. This addresses an apparent paradox since superluminality arises in the dual theory even when absent in the original one.
- May 15 2015 hep-th arXiv:1505.03750v3We show how conformal partial waves (or conformal blocks) of spinor/tensor correlators can be related to each other by means of differential operators in four dimensional conformal field theories. We explicitly construct such differential operators for all possible conformal partial waves associated to four-point functions of arbitrary traceless symmetric operators. Our method allows any conformal partial wave to be extracted from a few "seed" correlators, simplifying dramatically the computation needed to bootstrap tensor correlators.
- Dec 05 2014 hep-th arXiv:1412.1796v4We classify and compute, by means of the six-dimensional embedding formalism in twistor space, all possible three-point functions in four dimensional conformal field theories involving bosonic or fermionic operators in irreducible representations of the Lorentz group. We show how to impose in this formalism constraints due to conservation of bosonic or fermionic currents. The number of independent tensor structures appearing in any three-point function is obtained by a simple counting. Using the Operator Product Expansion (OPE), we can then determine the number of structures appearing in 4-point functions with arbitrary operators. This procedure is independent of the way we take the OPE between pairs of operators, namely it is consistent with crossing symmetry, as it should be. An analytic formula for the number of tensor structures for three-point correlators with two symmetric and an arbitrary bosonic (non-conserved) operators is found, which in turn allows to analytically determine the number of structures in 4-point functions of symmetric traceless tensors.
- We numerically study the crossing symmetry constraints in 4D CFTs, using previously introduced algorithms based on semidefinite programming. We study bounds on OPE coefficients of tensor operators as a function of their scaling dimension and extend previous studies of bounds on OPE coefficients of conserved vector currents to the product groups SO(N)xSO(M). We also analyze the bounds on the OPE coefficients of the conserved vector currents associated with the groups SO(N), SU(N) and SO(N)xSO(M) under the assumption that in the singlet channel no scalar operator has dimension less than four, namely that the CFT has no relevant deformations. This is motivated by applications in the context of composite Higgs models, where the strongly coupled sector is assumed to be a spontaneously broken CFT with a global symmetry.
- Mar 14 2014 hep-th astro-ph.CO arXiv:1403.3095v3Non-linear realizations of spacetime symmetries can be obtained by a generalization of the coset construction valid for internal ones. The physical equivalence of different representations for spacetime symmetries is not obvious, since their relation involves not only a redefinition of the fields but also a field-dependent change of coordinates. A simple and relevant spacetime symmetry is obtained by the contraction of the 4D conformal group that leads to the Galileon group. We analyze two non-linear realizations of this group, focusing in particular on the propagation of signals around non-trivial backgrounds. The aperture of the lightcone is in general different in the two representations and in particular a free (luminal) massless scalar is mapped in a Galileon theory which admits superluminal propagation. We show that in this theory, if we consider backgrounds that vanish at infinity, there is no asymptotic effect: the displacement of the trajectory integrates to zero, as can be expected since the S-matrix is trivial. Regarding local measurements, we show that the puzzle is solved taking into account that a local coupling with fixed sources in one theory is mapped into a non-local coupling and we show that this effect compensates the different lightcone. Therefore the two theories have a different notion of locality. The same applies to the different non-linear realizations of the conformal group and we study the particular case of a cosmologically interesting background: the Galilean Genesis scenarios.
- We study the consequences of combining SUSY with a pseudo Nambu-Goldstone boson Higgs coming from an SO(5)/SO(4) coset and partial compositeness. In particular, we focus on how electroweak symmetry breaking and the Higgs mass are reproduced in models where the symmetry SO(5) is linearly realized. The global symmetry forbids tree-level contributions to the Higgs potential coming from D-terms, differently from what happens in most of the SUSY little-Higgs constructions. While the stops are generally heavy, light fermion top partners below 1 TeV are predicted. In contrast to what happens in non-SUSY composite Higgs models, they are necessary to reproduce the correct top, rather than Higgs, mass. En passant, we point out that, independently of SUSY, models where tR is fully composite and embedded in the 5 of SO(5) generally predict a too light Higgs.
- There are two common non-linear realizations of the 4D conformal group: in the first, the dilaton is the conformal factor of the effective metric \eta_\mu\nu e^-2 \pi; in the second it describes the fluctuations of a brane in AdS_5. The two are related by a complicated field redefinition, found by Bellucci, Ivanov and Krivonos (2002) to all orders in derivatives. We show that this field redefinition can be understood geometrically as a change of coordinates in AdS_5. In one gauge the brane is rigid at a fixed radial coordinate with a conformal factor on the AdS_5 boundary, while in the other one the brane bends in an unperturbed AdS_5. This geometrical picture illuminates some aspects of the mapping between the two representations. We show that the conformal Galileons in the two representations are mapped into each other in a quite non-trivial way: the DBI action, for example, is mapped into a complete linear combination of all the five Galileons in the other representation. We also verify the equivalence of the dilaton S-matrix in the two representations and point out that the aperture of the dilaton light-cone around non-trivial backgrounds is not the same in the two representations.
- We construct UV completions of bottom-up models with a pseudo Nambu-Goldstone Boson (NGB) composite Higgs and partial compositeness, admitting a weakly coupled description of the composite sector. This is identified as the low energy description of an SO(N) supersymmetric gauge theory with matter fields in the fundamental of the group. The Higgs is a NGB associated to an SO(5)/SO(4) coset of a global symmetry group and is identified with certain components of matter fields in a Seiberg dual description of the theory. The Standard Model (SM) gauge fields are obtained by gauging a subgroup of the global group. The mass mixing between elementary SM and composite fermion fields advocated in partial compositeness arise from the flow in the IR of certain trilinear Yukawa couplings defined in the UV theory. We explicitly construct two models of this kind. Most qualitative properties of the bottom-up constructions are derived. The masses of gauge and fermion resonances in the composite sector are governed by different couplings and can naturally be separated. Accommodating all SM fermion masses within the partial compositeness paradigm remains the main open problem, since the SM gauge couplings develop Landau poles at unacceptably low energies.
- We analyze if and to what extent the high energy behaviour of five-dimensional (5D) gauge theories can be improved by adding certain higher dimensional operators of "Lifshitz" type, without breaking the ordinary four-dimensional Lorentz symmetries. We show that the UV behaviour of the transverse gauge field polarizations can be improved by the Lifshitz operators, while the longitudinal polarizations get strongly coupled at energies lower than the ones in ordinary 5D theories, spoiling the usefulness of the construction in non-abelian gauge theories. We conclude that the improved behaviour as effective theories of the ordinary 5D models is not only related to locality and 5D gauge symmetries, but is a special property of the standard theories defined by the lowest dimensional operators.
- We introduce a scenario of lepton mixing in holographic composite Higgs models based on non-abelian discrete symmetries of the form G_f=X x Z_N, broken to Z_2 x Z_2 x Z_N in the elementary sector and to Z_N^(D) in the composite sector with Z_N^(D) being the diagonal subgroup of a Z_N contained in X and the external Z_N. By choosing X = Delta(96) or Delta(384), a non-vanishing theta_13 of order 0.1 is naturally obtained. We apply our considerations to a 5D model in warped space for the particular cases of X = S_4, A_5, Delta(96) and Delta(384) and N=3 or 5. Lepton flavour violating processes and electric dipole moments are well below the current bounds, with the exception of mu -> e gamma that puts a very mild constraint on the parameter space of the model, for all presented choices of G_f.
- We study leptons in holographic composite Higgs models, namely in models possibly admitting a weakly coupled description in terms of five-dimensional (5D) theories. We introduce two scenarios leading to Majorana or Dirac neutrinos, based on the non-abelian discrete group $S_4\times \Z_3$ which is responsible for nearly tri-bimaximal lepton mixing. The smallness of neutrino masses is naturally explained and normal/inverted mass ordering can be accommodated. We analyze two specific 5D gauge-Higgs unification models in warped space as concrete examples of our framework. Both models pass the current bounds on Lepton Flavour Violation (LFV) processes. We pay special attention to the effect of so called boundary kinetic terms that are the dominant source of LFV. The model with Majorana neutrinos is compatible with a Kaluza-Klein vector mass scale $m_{KK}\gtrsim 3.5$ TeV, which is roughly the lowest scale allowed by electroweak considerations. The model with Dirac neutrinos, although not considerably constrained by LFV processes and data on lepton mixing, suffers from a too large deviation of the neutrino coupling to the $Z$ boson from its Standard Model value, pushing $m_{KK}\gtrsim 10$ TeV.
- We construct new composite Higgs/gauge-Higgs unification (GHU) models in flat space that overcome all the difficulties found in the past in attempting to construct models of this sort. The key ingredient is the introduction of large boundary kinetic terms for gauge (and fermion) fields. We focus our analysis on the electroweak symmetry breaking pattern and the electroweak precision tests and show how both are compatible with each other. Our models can be seen as effective TeV descriptions of analogue warped models. We point out that, as far as electroweak TeV scale physics is concerned, one can rely on simple and more flexible flat space models rather than considering their unavoidably more complicated warped space counterparts. The generic collider signatures of our models are essentially undistinguishable from those expected from composite Higgs/warped GHU models, namely a light Higgs, colored fermion resonances below the TeV scale and sizable deviations to the Higgs and top coupling.
- We construct a Lifshitz-like version of five-dimensional (5D) QED which is UV - completed and reduces at low energies to ordinary 5D QED. The UV quantum behaviour of this theory is very smooth. In particular, the gauge coupling constant is finite at all energy scales and at all orders in perturbation theory. We study the IR properties of this theory, when compactified on a circle, and compare the one-loop energy dependence of the coupling in the Lifshitz theory with that coming from the standard 5D QED effective field theory. The range of validity of the 5D effective field theory is found to agree with the more conservative version of Naive Dimensional Analysis.
- I review the holographic techniques used to efficiently study models with Gauge-Higgs Unification (GHU) in one extra dimension. The general features of GHU models in flat extra dimensions are then reviewed, emphasizing the aspects related to electroweak symmetry breaking. Two potentially realistic models, based on SU(3) and SO(5) electroweak gauge groups, respectively, are constructed.
- We study the one-loop renormalization and evolution of the couplings in scalar field theories of the Lifshitz type, i.e. with different scaling in space and time. These theories are unitary and renormalizable, thanks to higher spatial derivative terms that modify the particle propagator at high energies, but at the expense of explicitly breaking Lorentz symmetry. We study if and under what conditions the Lorentz symmetry can be considered as emergent at low energies by studying the RG evolution of the ``speed of light'' coupling $c^2_\phi$ and, for more than one field, of $\delta c^2\equiv c^2_{\phi_1}-c^2_{\phi_2}$ in simple models. We find that in the UV both $c^2_\phi$ and $\delta c^2$ generally flow logarithmically with the energy scale. A logarithmic running of $c^2$ persists also at low-energies, if $\delta c^2 \neq 0$ in the UV. As a result, Lorentz symmetry is not recovered at low energies with the accuracy needed to withstand basic experimental constraints, unless all the Lorentz breaking terms, including $\delta c^2$, are unnaturally fine-tuned to extremely small values in the UV. We expect that the considerations of this paper will apply to any generic theory of Lifshitz type, including a recently proposed quantum theory of gravity by Horava.
- We continue our analysis of establishing the reliability of "simple" effective theories where massive fields are "frozen" rather than integrated out, in a wide class of four dimensional theories with global or local N=1 supersymmetry. We extend our previous work by adding gauge fields and O(1) Yukawa-like terms for the charged fields in the superpotential. For generic Kaehler potentials, a meaningful freezing is allowed for chiral multiplets only, whereas in general heavy vector fields have to properly be integrated out. Heavy chiral fields can be frozen if they approximately sit to supersymmetric solutions along their directions and, in supergravity, if the superpotential at the minimum is small, so that a mass hierarchy between heavy and light fields is ensured. When the above conditions are met, we show that the simple effective theory is generally a reliable truncation of the full one.
- We study under what conditions massive fields can be "frozen" rather than integrated out in certain four dimensional theories with global or local N=1 supersymmetry. We focus on models without gauge fields, admitting a superpotential of the form W = W0(H) + epsilon W1(H,L), with epsilon << 1, where H and L schematically denote the heavy and light chiral superfields. We find that the fields H can always be frozen to constant values H0, if they approximately correspond to supersymmetric solutions along the H directions, independently of the form of the Kahler potential K for H and L, provided K is sufficiently regular. In supergravity W0 is required to be of order epsilon at the vacuum to ensure a mass hierarchy between H and L. The backreaction induced by the breaking of supersymmetry on the heavy fields is always negligible, leading to suppressed F^H--terms. For factorizable Kahler potentials W0 can instead be generic. Our results imply that the common way complex structure and dilaton moduli are stabilized, as in Phys. Rev. D 68 (2003) 046005 by Kachru et al., for instance, is reliable to a very good accuracy, provided W0 is small enough.
- We study how two moduli can be stabilized in a Minkowski/de Sitter vacuum for a wide class of string-inspired Supergravity models with an effective Fayet-like Supersymmetry breaking. It is shown under which conditions this mechanism can be made natural and how it can give rise to an interesting spectrum of soft masses, with a relatively small mass difference between scalar and gaugino masses. In absence of a constant superpotential term, the above mechanism becomes completely natural and gives rise to a dynamical supersymmetry breaking mechanism. Some specific type IIB and heterotic string inspired models are considered in detail.
- We show that a discrete exchange symmetry can give rise to realistic dark matter candidates in models with warped extra dimensions. We show how to realize our construction in a variety of models with warped extra dimensions and study in detail a realistic model of Gauge-Higgs Unification/composite Higgs in which the observed amount of dark matter is naturally reproduced. In this model, a realistic pattern of electroweak symmetry breaking typically occurs in a region of parameter space in which the fit to the electroweak precision observables improves, the Higgs is heavier than the experimental bound and new light quark resonances are predicted. We also quantify the fine-tuning of such scenarios, and discuss in which sense Gauge-Higgs Unification models result in a natural theory of electroweak symmetry breaking.
- We revisit the issue of moduli stabilization in a class of N=1 four dimensional supergravity theories which are low energy descriptions of standard perturbative heterotic string vacua compactified on Calabi-Yau spaces. In particular, we show how it is possible to stabilize the universal dilaton and Kahler moduli in a de Sitter/Minkowski vacuum with low energy supersymmetry breaking by means of non-perturbative gauge dynamics, including recent results by Intriligator, Seiberg and Shih. The non-SUSY vacua are meta-stable but sufficiently long-lived.
- We show that a recently constructed five-dimensional (5D) model with gauge-Higgs unification and explicit Lorentz symmetry breaking in the bulk, provides a natural dark matter candidate. This is the lightest Kaluza-Klein particle odd under a certain discrete Z_2 symmetry, which has been introduced to improve the naturalness of the model, and resembles KK-parity but is less constraining. The dark matter candidate is the first KK mode of a 5D gauge field and electroweak bounds force its mass above the TeV scale. Its pair annihilation rate is too small to guarantee the correct relic abundance; however coannihilations with colored particles greatly enhance the effective annihilation rate, leading to realistic relic densities.
- We perform a complete study of flavour and CP conserving electroweak observables in a slight refinement of a recently proposed five--dimensional model on R^4XS^1/Z_2, where the Higgs is the internal component of a gauge field and the Lorentz symmetry is broken in the fifth dimension. Interestingly enough, the relevant corrections to the electroweak observables turn out to be of universal type and essentially depend only on the value of the Higgs mass and on the scale of new physics, in our case the compactification scale 1/R. The model passes all constraints for 1/R > 4.7 TeV at 90% C.L., with a moderate fine--tuning in the parameters. The Higgs mass turns out to be always smaller than 200 GeV although higher values would be allowed, due to a large correction to the T parameter. The lightest non-SM states in the model are typically colored fermions with a mass of order 1-2 TeV.
- Dec 22 2005 hep-th arXiv:hep-th/0512272v2We revisit the T-duality transformation rules in heterotic string theory, pointing out that the chiral structure of the world-sheet leads to a modification of the standard Buscher's transformation rules. The simplest instance of such modifications arises for toroidal compactifications, which are rederived by analyzing a bosonized version of the heterotic world-sheet Lagrangian. Our study indicates that the usual heterotic toroidal T-duality rules naively extended to the curved case cannot be correct, leading in particular to an incorrect Bianchi identity for the field strength H of the Kalb-Ramond field B. We explicitly show this problem and provide a specific example of dual models where we are able to get new T-duality rules which, contrary to the standard ones, lead to a correct T-dual Bianchi identity for H to all orders in \alpha'.
- We reconsider the idea of identifying the Higgs field as the internal component of a gauge field in the flat space R^4XS^1/Z_2, by relaxing the constraint of having unbroken SO(4,1) Lorentz symmetry in the bulk. In this way, we show that the main common problems of previous models of this sort, namely the prediction of a too light Higgs and top mass, as well as of a too low compactification scale, are all solved. We mainly focus our attention on a previously constructed model. We show how, with few minor modifications and by relaxing the requirement of SO(4,1) symmetry, a potentially realistic model can be obtained with a moderate tuning in the parameter space of the theory. In this model, the Higgs potential is stabilized and the hierarchy of fermion masses explained.
- I review, at a general non-technical level, the main properties of models in extra dimensions where the Higgs field is identified with some internal component of a gauge field.
- The dynamics of five dimensional Wilson line phases at finite temperature is studied in the one-loop approximation. We show that at temperatures of order T ∼1/L, where L is the length of the compact space, the gauge symmetry is always restored and the electroweak phase transition appears to be of first order. Particular attention is devoted to the study of a recently proposed five dimensional orbifold model (on S1/Z2) where the Wilson line phase is identified with the Higgs field (gauge-Higgs unification). Interestingly enough, an estimate of the leading higher-loop ``daisy'' (or ``ring'') diagram contributions to the effective potential in a simple five dimensional model, seems to suggest that the electroweak phase transition can be studied in perturbation theory even for Higgs masses above the current experimental limit of 114 GeV. The transition is still of first order for such values of the Higgs mass. If large localized gauge kinetic terms are present, the transition might be strong enough to give baryogenesis at the electroweak transition.
- We study the Dirac equation of chiral fermions on a regularized version of the two-dimensional T^2/Z_2 orbifold, where the conical singularities are replaced by suitable spherical caps with constant curvature. This study shows how localized and bulk fermions arise in the orbifold as the resolved space approaches the orbifold limit. Our analysis also shows that not all possible fermion configurations on T^2/Z_2 admit such a simple resolution. We focus our study to a fermion coupled to a U(1) gauge field. It is explicitly shown how a resolution of the orbifold puts severe constraints on the allowed chiralities and U(1) charges of the massless four dimensional fermions, localized or not, that can be present in the orbifold. The limit in which T^2/Z_2 (and its corresponding resolved space) collapses to S^1/Z_2 is also studied in detail.
- We give an overview of the issue of anomalies in field theories with extra dimensions. We start by reviewing in a pedagogical way the computation of the standard perturbative gauge and gravitational anomalies on non-compact spaces, using Fujikawa's approach and functional integral methods, and discuss the available mechanisms for their cancellation. We then generalize these analyses to the case of orbifold field theories with compact internal dimensions, emphasizing the new aspects related to the presence of orbifold singularities and discrete Wilson lines, and the new cancellation mechanisms that are becoming available. We conclude with a very brief discussion on global and parity anomalies.
- Six-dimensional orbifold models where the Higgs field is identified with some internal component of a gauge field are considered. We classify all possible T^2/Z_N orbifold constructions based on a SU(3) electroweak gauge symmetry. Depending on the orbifold twist, models with two, one or zero Higgs doublets can be obtained. Models with one Higgs doublet are particularly interesting because they lead to a prediction for the Higgs mass, which is twice the W boson mass at leading order: m_H=2 m_W. The electroweak scale is quadratically sensitive to the cut-off, but only through very specific localized operators. We study in detail the structure of these operators at one loop, and identify a class of models where they do not destabilize the electroweak scale at the leading order. This provides a very promising framework to construct realistic and predictive models of electroweak symmetry breaking.
- A precise correspondence between freely-acting orbifolds (Scherk-Schwarz compactifications) and string vacua with NSNS flux turned on is established using T-duality. We focus our attention to a certain non-compact Z_2 heterotic freely-acting orbifold with N=2 supersymmetry (SUSY). The geometric properties of the T-dual background are studied. As expected, the space is non-Kahler with the most generic torsion compatible with SUSY. All equations of motion are satisfied, except the Bianchi identity for the NSNS field, that is satisfied only at leading order in derivatives, i.e. without the curvature term. We point out that this is due to unknown corrections to the standard heterotic T-duality rules.
- We study higher-dimensional non-supersymmetric orbifold models where the Higgs field is identified with some internal component of a gauge field. We address two important and related issues that constitute severe obstacles towards model building within this type of constructions: the possibilities of achieving satisfactory Yukawa couplings and Higgs potentials. We consider models where matter fermions are localized at the orbifold fixed-points and couple to additional heavy fermions in the bulk. When integrated out, the latter induce tree-level non-local Yukawa interactions and a quantum contribution to the Higgs potential that we explicitly evaluate and analyse. The general features of these highly constrained models are illustrated through a minimal but potentially realistic five-dimensional example. Finally, we discuss possible cures for the persisting difficulties in achieving acceptable top and Higgs masses. In particular, we consider in some detail the effects induced in these models by adding localized kinetic terms for gauge fields.
- We study string-gas cosmology in dilaton gravity, inspired by the fact that it naturally arises in a string theory context. Our main interest is the thermodynamical treatment of the string-gas and the resulting implications for the cosmology. Within an adiabatic approximation, thermodynamical equilibrium and a small, toroidal universe as initial conditions, we numerically solve the corresponding equations of motions in two different regimes describing the string-gas thermodynamics: (i) the Hagedorn regime, with a single scale factor, and (ii) an almost-radiation dominated regime, which includes the leading corrections due to the lightest Kaluza Klein and winding modes, with two scale factors. The scale factor in the Hagedorn regime exhibits very slow time evolution with nearly constant energy and negligible pressure. By contrast, in case (ii) we find interesting cosmological solutions where the large dimensions continue to expand and the small ones are kept undetectably small.
- We study the quantum stability of Type IIB orbifold and orientifold string models in various dimensions, including Melvin backgrounds, where supersymmetry (SUSY) is broken \it à la Scherk-Schwarz (SS) by twisting periodicity conditions along a circle of radius R. In particular, we compute the R-dependence of the one-loop induced vacuum energy density $\rho(R)$, or cosmological constant. For SS twists different from Z2 we always find, for both orbifolds and orientifolds, a monotonic $\rho(R)<0$, eventually driving the system to a tachyonic instability. For Z2 twists, orientifold models can have a different behavior, leading either to a runaway decompactification limit or to a negative minimum at a finite value R_0. The last possibility is obtained for a 4D chiral orientifold model where a more accurate but yet preliminary analysis seems to indicate that $R_0\to \infty$ or towards the tachyonic instability, as the dependence on the other geometric moduli is included.
- We discuss the generalization to global gauge anomalies of the familiar procedure for the cancellation of local gauge anomalies in effective theories of spontaneously broken symmetries. We illustrate this mechanism in a recently proposed six-dimensional extension of the standard model.
- We study examples of chiral four-dimensional IIB orientifolds with Scherk--Schwarz supersymmetry breaking, based on freely acting orbifolds. We construct a new Z3xZ3' model, containing only D9-branes, and rederive from a more geometric perspective the known Z6'xZ2' model, containing D9, D5 and \bar D 5 branes. The cancellation of anomalies in these models is then studied locally in the internal space. These are found to cancel through an interesting generalization of the Green--Schwarz mechanism involving twisted Ramond--Ramond axions and 4-forms. The effect of the latter amounts to local counterterms from a low-energy effective field theory point of view. We also point out that the number of spontaneously broken U(1) gauge fields is in general greater than what expected from a four-dimensional analysis of anomalies.
- We study the constraints on models with extra dimensions arising from local anomaly cancellation. We consider a five-dimensional field theory with a U(1) gauge field and a charged fermion, compactified on the orbifold S^1/(Z_2 x Z_2'). We show that, even if the orbifold projections remove both fermionic zero modes, there are gauge anomalies localized at the fixed points. Anomalies naively cancel after integration over the fifth dimension, but gauge invariance is broken, spoiling the consistency of the theory. We discuss the implications for realistic supersymmetric models with a single Higgs hypermultiplet in the bulk, and possible cancellation mechanisms in non-minimal models.
- We construct a general class of chiral four-dimensional string models with Scherk--Schwarz supersymmetry breaking, involving freely acting orbifolds. The basic ingredient is to combine an ordinary supersymmetry-preserving Z_N projection with a supersymmetry-breaking projection Z_M' acting freely on a subspace of the internal manifold. A crucial condition is that any generator of the full orbifold group Z_N x Z_M' must either preserve some supersymmetry or act freely in order to become irrelevant in some large volume limit. Tachyons are found to be absent or limited to a given region of the tree-level moduli space. We find several new models with orthogonal supersymmetries preserved at distinct fixed-points. Particular attention is devoted to an interesting Z_3 x Z_3' heterotic example.
- Scherk-Schwarz gauge symmetry breaking of a D-dimensional field theory model compactified on a circle is analyzed. It is explicitly shown that forbidden couplings in the unbroken theory appear in the one-loop effective action only in a non-local way, implying that they are finite at all orders in perturbation theory. This result can be understood as a consequence of the local gauge symmetry, but it holds true also in the global limit.
- Dec 15 2000 hep-th arXiv:hep-th/0012124v1We present a complete string theory analysis of all mixed gauge, gravitational and target-space anomalies potentially arising in the simplest heterotic Z_N orbifold models, with N odd and standard embedding. These anomalies turn out to be encoded in an elliptic index, which can be easily computed; they are found to cancel through a universal GS mechanism induced by the dilaton multiplet. The target-space symmetry is then shown to have a nice geometric interpretation in terms of torsion, and the target-space dependence of the four-dimensional GS couplings can be alternatively rederived from the implicit torsion dependence of the standard ten-dimensional GS couplings. The result is universal and consists essentially of a Bianchi identity for the NSNS B field depending on all the curvatures, and in particular on the target-space curvature.
- Oct 05 2000 hep-th arXiv:hep-th/0010022v3The dependence on the torsion H=db of the Wess-Zumino couplings of D-branes that are trivially embedded in space-time is studied. We show that even in this simple set-up some torsion components can be turned on, with a non-trivial effect on the RR couplings. In the special cases in which either the tangent or the normal bundle are trivial, the torsion dependence amounts to substitute the standard curvature with its generalization in the presence of torsion, in the usual couplings involving the roof genus A.
- Jun 27 2000 hep-th arXiv:hep-th/0006201v3We investigate in the simplest compact D=4 N=1 Type IIB orientifold models the sigma-model symmetry suggested by the proposed duality of these models to heterotic orbifold vacua. This symmetry is known to be present at the classical level, and is associated to a composite connection involving untwisted moduli in the low-energy supergravity theory. In order to study possible anomalies arising at the quantum level, we compute potentially anomalous one-loop amplitudes involving gluons, gravitons and composite connections. We argue that the effective vertex operator associated to the composite connection has the same form as that for a geometric deformation of the orbifold. Assuming this, we are able to compute the complete anomaly polynomial, and find that all the anomalies are canceled through a Green-Schwarz mechanism mediated by twisted RR axions, as previously conjectured. Some questions about the field theory interpretation of our results remain open.
- Dec 15 1999 hep-th arXiv:hep-th/9912108v2The cancellation of U(1)-gauge and U(1)-gravitational anomalies in certain D=4 N=1 Type IIB orientifolds is analyzed in detail, from a string theory point of view. We verify the proposal that these anomalies are cancelled by a Green-Schwarz mechanism involving only twisted Ramond-Ramond fields. By factorizing one-loop partition functions, we also get the anomalous couplings of D-branes, O-planes and orbifold fixed-points to these twisted fields. Twisted sectors with fixed-planes participate to the inflow mechanism in a peculiar way.
- Nov 30 1999 hep-th arXiv:hep-th/9911223v1We review the anomaly inflow mechanism on D-branes and O-planes. In particular, we compute the one-loop world-volume anomalies and derive the RR anomalous couplings required for their cancellation.
- Jul 15 1999 hep-th arXiv:hep-th/9907112v3We study in detail the pattern of anomaly cancellation in D=6 Type IIB Z_N orientifolds, occurring through a generalized Green-Schwarz mechanism involving several RR antisymmetric tensors and scalars fields. The starting point is a direct string theory computation of the inflow of anomaly arising from magnetic interaction of D-branes, O-planes and fixed-points, which are encoded in topological one-loop partition functions in the RR odd spin-structure. All the RR anomalous couplings of these objects are then obtained by factorization. They are responsible for a spontaneous breaking of U(1) factors through a Higgs mechanism involving the corresponding hypermultiplets. Some of them are also related by supersymmetry to gauge couplings involving the NSNS scalars sitting in the tensor multiplets. We also comment on the possible occurrence of tensionless strings when these couplings diverge.
- May 26 1999 hep-th arXiv:hep-th/9905183v1The leading eikonal S-matrix for three graviton scattering in d=11 supergravity and Matrix Theory are shown to precisely agree. The result unifies the source-probe plus recoil approach of Okawa and Yoneya and relaxes the restriction imposed by those authors that all D-particle impact parameters and velocities are mutually perpendicular. Furthermore, the unified S-matrix approach facilitates a clean-cut study of M-theoretic R^4 curvature corrections to the low energy supergravity effective action. In particular, the leading R^4 correction to the three graviton S-matrix is computed and compared to the corresponding next to leading order two loop U(3) amplitude in Matrix Theory. We find a clear disagreement of the two resulting tensor structures.
- Mar 17 1999 hep-th arXiv:hep-th/9903145v1We derive the general form of the anomaly for chiral spinors and self-dual antisymmetric tensors living on D-brane and O-plane interesections, using both path-integral and index theorem methods. We then show that the anomalous couplings to RR forms of D-branes and O-planes in a general background are precisely those required to cancel these anomalies through the inflow mechanism. This allows, for instance, for local anomaly cancellation in generic orientifold models, the relevant Green-Schwarz term being given by the sum of the anomalous couplings of all the D-branes and O-planes in the model.
- Mar 12 1999 hep-th arXiv:hep-th/9903099v1We briefly review the computation of graviton and antisymmetric tensor scattering amplitudes in Matrix Theory from a diagramatic S-Matrix point of view.
- Dec 09 1998 hep-th arXiv:hep-th/9812071v1We study anomalous Wess-Zumino couplings of D-branes and O-planes in a general background and derive them from a direct string computation by factorizing in the RR channel various one-loop amplitudes. In particular, we find that Op-planes present gravitational anomalous couplings involving the Hirzebruch polynomial L, similarly to the roof genus A encoding Dp-brane anomalous couplings. We determine, in each case, the precise dependence of these couplings on the curvature of the tangent and normal bundles.
- Dec 07 1998 hep-th arXiv:hep-th/9812039v1Spin interactions beteween two moving Dp-branes are analyzed using the Green-Schwarz formalism of boundary states. This approach turns out to be extremely efficient to compute all the spin effects related by supersymmetry to the leading v^4/r^7-p term. All these terms are shown to be scale invariant, supporting a matrix model description of supergravity interactions. By employing the LSZ reduction formula for matrix theory and the mentioned supersymmetric effective potential for D0-branes, we compute the t-pole of graviton-graviton and three form-three form scattering in matrix theory. The results are found to be in complete agreement with tree level supergravity in the corresponding kinematical regime and provide, moreover, an explicit map between these degrees of freedom in both theories.
- Sep 11 1998 hep-th arXiv:hep-th/9809070v2We employ the LSZ reduction formula for Matrix Theory introduced in our earlier work to compute the t-pole S-matrix for three form-three form scattering. The result agrees completely with tree level D=11 SUGRA. Taken together with previous results on graviton-graviton scattering this shows that Matrix Theory indeed reproduces the bosonic sector of the D=11 SUGRA action including the Chern-Simons term. Furthermore we provide a detailed account of our framework along with the technology to compute any Matrix Theory one-loop t-pole scattering amplitude at vanishing p^- exchange.
- Jun 12 1998 hep-th arXiv:hep-th/9806081v1The technology required for eikonal scattering amplitude calculations in Matrix theory is developed. Using the entire supersymmetric completion of the v^4/r^7 Matrix theory potential we compute the graviton-graviton scattering amplitude and find agreement with eleven dimensional supergravity at tree level.
- Jan 29 1998 hep-th arXiv:hep-th/9801183v3We study spin interactions between two moving D-branes using the Green-Schwarz formalism of boundary states. We focus our attention on the leading terms for small velocities v, of the form v^4-n/r^7-p+n (v^2-n/r^3-p+n) for p-p (p-p+4) systems, with 16 (8) supercharges. In analogy with standard G-S computations of massless four-point one-loop amplitudes in Type I theory, the above terms are governed purely by zero modes, massive states contributions cancelling as expected by the residual supersymmetry. This implies the scale invariance of these leading spin-effects, supporting the relevant matrix model descriptions of supergravity interactions; in this context, we also discuss similar results for more general brane configurations. We then give a field theory interpretation of our results, that allows in particular to deduce the gyromagnetic ratio g=1 and the presence of a quadrupole moment for D0-branes.
- Nov 06 1997 hep-th arXiv:hep-th/9711031v2By scaling arguments we show that the presence of a $R^4$-term in the eleven dimensional supergravity effective lagrangian, if it is visible in (M)atrix theory, should produce a correction to the five-loops effective lagrangian of two moving D0-branes.
- Sep 09 1997 hep-th arXiv:hep-th/9709063v2We study the spin dependence of D-brane dynamics in the Green-Schwarz formalism of boundary states. In particular we show how to interpret insertion of supercharges on the boundary state as sources of non-universal spin effects in D-brane potentials. In this way we find for a generic (D)p-brane, potentials going like $v^{4-n}/r^{7-p+n}$ corresponding to interactions between the different components of the D-brane supermultiplet. From the eleven dimensional point of view, these potentials arise from the exchange of field strengths corresponding to the graviton and the three form, coupled non-minimally to the branes. We show how an annulus computation truncated to its massless contribution is enough to reproduce these next-to-leading effects, meaning in particular that the one-loop (M)atrix theory effective action should encode all the spin dependence of low-energy supergravity interactions.
- Mar 07 1997 hep-th arXiv:hep-th/9703049v2We study the moduli dependence of a class of couplings in $K3\times T^2$ compactifications of type I string theory, for which one-loop amplitudes can be written in terms of an N=2 supersymmetric index. This index is determined for generic models as a function of the BPS spectrum. As an application we compute the one-loop moduli dependence of the $F_g W^{2g}$ couplings, where W is the N=2 gravitational superfield, for type I compactifications based on the Gimon-Johnson K3 orientifolds, showing explicitly their dependence on the aforementioned index.
- Nov 06 1996 hep-th arXiv:hep-th/9611017v2We test the conjectured Type I-Heterotic Duality in four dimensions by analyzing a given class of higher derivative F-terms of the form $F_gW^{2g}$, with W the N=2 gravitational superfield. We study a particular dual pair of theories, the O(2,2) heterotic model and a type I model based on the K3 $Z_2$ orbifold theory constructed by Gimon and Polchinski, further compactified on a torus. The $F_g$ couplings appear at 1-loop on both theories; because of the weak-weak nature of this duality in four dimensions, it is meaningful to compare the heterotic $F_g$'s with the corresponding type I couplings perturbatively. We compute the $F_g$'s in type I, showing that they receive contributions only from N=2 BPS states and that in the appropriate limit they coincide with the heterotic couplings, in agreement with the given duality.
- Jul 26 1996 hep-th arXiv:hep-th/9607193v1We study a special class of higher derivative F-terms of the form $F_{g,n}W^{2g}(\Pi f)^{n}$ where W is the N=2 gravitational superfield and $\Pi$ is the chiral projector applied to a non-holomorphic function $f$ of the heterotic dilaton vector superfield. We analyze these couplings in the heterotic theory on $K3\times T^2$ , where it is found they satisfy an anomaly equation as the well studied $F_{g,0}$ terms. We recognize that, near a point of SU(2) enhancement, a given generating function of the leading singularity of the $F_{g,n}$ reproduces the free energy of a c=1 string at an arbitrary radius R. According to the N=2 heterotic-type II duality in 4d, we then study these couplings near a conifold singularity, using its local description in terms of intersecting D-5-branes. In this context, it turns out that there exists, among the other states involved, a vector gauge field reproducing the heterotic leading singularity structure.