arXiv subjects

Guido Festuccia

Publications and source records attributed to Guido Festuccia.

At least 37 records · Page 2Linked to original sources

arXiv2012

Exploring Curved Superspace (II)

We extend our previous analysis of Riemannian four-manifolds M admitting rigid supersymmetry to N=1 theories that do not possess a U(1)_R symmetry. With one exception, we find that M must be a Hermitian manifold. However, the presence of supersymmetry imposes additional restrictions. For instance, a supercharge that squares to zero exists, if the canonical bundle of the Hermitian manifold M admits a nowhere vanishing, holomorphic section. This requirement can be slightly relaxed if M is a torus bundle over a Riemann surface, in which case we obtain a supercharge that squares to a complex Killing vector. We also analyze the conditions for the presence of more than one supercharge. The exceptional case occurs when M is a warped product S^3 x R, where the radius of the round S^3 is allowed to vary along R. Such manifolds admit two supercharges that generate the superalgebra OSp(1|2). If the S^3 smoothly shrinks to zero at two points, we obtain a squashed four-sphere, which is not a Hermitian manifold.

hep-th↗

arXiv2012

Exploring Curved Superspace

We systematically analyze Riemannian manifolds M that admit rigid supersymmetry, focusing on four-dimensional N=1 theories with a U(1)_R symmetry. We find that M admits a single supercharge, if and only if it is a Hermitian manifold. The supercharge transforms as a scalar on M. We then consider the restrictions imposed by the presence of additional supercharges. Two supercharges of opposite R-charge exist on certain fibrations of a two-torus over a Riemann surface. Upon dimensional reduction, these give rise to an interesting class of supersymmetric geometries in three dimensions. We further show that compact manifolds admitting two supercharges of equal R-charge must be hyperhermitian. Finally, four supercharges imply that M is locally isometric to M_3 x R, where M_3 is a maximally symmetric space.

hep-th↗

arXiv2012

Contact Terms, Unitarity, and F-Maximization in Three-Dimensional Superconformal Theories

We consider three-dimensional N=2 superconformal field theories on a three-sphere and analyze their free energy F as a function of background gauge and supergravity fields. A crucial role is played by certain local terms in these background fields, including several Chern-Simons terms. The presence of these terms clarifies a number of subtle properties of F. This understanding allows us to prove the F-maximization principle. It also explains why computing F via localization leads to a complex answer, even though we expect it to be real in unitary theories. We discuss several corollaries of our results and comment on the relation to the F-theorem.

hep-th↗

arXiv2011

Rigid Supersymmetric Theories in Curved Superspace

We present a uniform treatment of rigid supersymmetric field theories in a curved spacetime $\mathcal{M}$, focusing on four-dimensional theories with four supercharges. Our discussion is significantly simpler than earlier treatments, because we use classical background values of the auxiliary fields in the supergravity multiplet. We demonstrate our procedure using several examples. For $\mathcal{M}=AdS_4$ we reproduce the known results in the literature. A supersymmetric Lagrangian for $\mathcal{M}=\mathbb{S}^4$ exists, but unless the field theory is conformal, it is not reflection positive. We derive the Lagrangian for $\mathcal{M}=\mathbb{S}^3\times \mathbb{R}$ and note that the time direction $\mathbb{R}$ can be rotated to Euclidean signature and be compactified to $\mathbb{S}^1$ only when the theory has a continuous R-symmetry. The partition function on $\mathcal{M}=\mathbb{S}^3\times \mathbb{S}^1$ is independent of the parameters of the flat space theory and depends holomorphically on some complex background gauge fields. We also consider R-invariant $\mathcal{N}=2$ theories on $\mathbb{S}^3$ and clarify a few points about them.

hep-th↗

arXiv2011

Supersymmetric QCD: Exact Results and Strong Coupling

We revisit two longstanding puzzles in supersymmetric gauge theories. The first concerns the question of the holomorphy of the coupling, and related to this the possible definition of an exact (NSVZ) beta function. The second concerns instantons in pure gluodynamics, which appear to give sensible, exact results for certain correlation functions, which nonetheless differ from those obtained using systematic weak coupling expansions. For the first question, we extend an earlier proposal of Arkani-Hamed and Murayama, showing that if their regulated action is written suitably, the holomorphy of the couplings is manifest, and it is easy to determine the renormalization scheme for which the NSVZ formula holds. This scheme, however, is seen to be one of an infinite class of schemes, each leading to an exact beta function; the NSVZ scheme, while simple, is not selected by any compelling physical consideration. For the second question, we explain why the instanton computation in the pure supersymmetric gauge theory is not reliable, even at short distances. The semiclassical expansion about the instanton is purely formal; if infrared divergences appear, they spoil arguments based on holomorphy. We demonstrate that infrared divergences do not occur in the perturbation expansion about the instanton, but explain that there is no reason to think this captures all contributions from the sector with unit topological charge. That one expects additional contributions is illustrated by dilute gas corrections. These are infrared divergent, and so difficult to define, but if non-zero give order one, holomorphic, corrections to the leading result. Exploiting an earlier analysis of Davies et al, we demonstrate that in the theory compactified on a circle of radius beta, due to infrared effects, finite contributions indeed arise which are not visible in the formal limit that beta goes to infinity.

hep-th↗

arXiv2010

Axions in the Landscape and String Theory

While axions seem ubiquitous in critical string theories, whether they might survive in any string theoretic description of nature is a difficult question. With some mild assumptions, one can frame the issues in the case that there is an approximate supersymmetry below the underlying string scale. The problem of axions is then closely tied to the question of how moduli are fixed. We consider, from this viewpoint, the possibility that supersymmetry is broken at an intermediate scale, as in "gravity mediation," at a low scale, as in gauge mediation, and at a very high scale, to model the possibility that there is no low energy supersymmetry. Putative mechanisms for moduli fixing can then be systematically classified, and at least for intermediate and high scale breaking, light axions appear plausible. In the course of this work, we are lead to consider aspects of moduli fixing and supersymmetry breaking, and we revisit the possibility of very large extra dimensions.

hep-th↗

arXiv2010

Reliable Semiclassical Computations in QCD

We revisit the question of whether or not one can perform reliable semiclassical QCD computations at zero temperature. We study correlation functions with no perturbative contributions, and organize the problem by means of the operator product expansion, establishing a precise criterion for the validity of a semiclassical calculation. For $N_f>N$, a systematic computation is possible; for $N_f<N$, it is not. $N_f=N$ is a borderline case. In our analysis, we see explicitly the exponential suppression of instanton effects at large $N$. As an application, we describe a test of QCD lattice gauge theory computations in the chiral limit.

hep-th↗

arXiv2010

The Regge Limit for Green Functions in Conformal Field Theory

We define a Regge limit for off-shell Green functions in quantum field theory, and study it in the particular case of conformal field theories (CFT). Our limit differs from that defined in arXiv:0801.3002, the latter being only a particular corner of the Regge regime. By studying the limit for free CFTs, we are able to reproduce the Low-Nussinov, BFKL approach to the pomeron at weak coupling. The dominance of Feynman graphs where only two high momentum lines are exchanged in the t-channel, follows simply from the free field analysis. We can then define the BFKL kernel in terms of the two point function of a simple light-like bilocal operator. We also include a brief discussion of the gravity dual predictions for the Regge limit at strong coupling.

hep-th↗

arXiv2010

Axions in Gauge Mediation

In supersymmetric theories, the presence of axions usually implies the existence of a non-compact, (pseudo)moduli space. In gauge mediated models, the axion would seem a particularly promising dark matter candidate. The cosmology of the moduli then constrains the gravitino mass and the axion decay constant; the former can't be much below 10 MeV; the latter can't be much larger than 10^{13} GeV. Axinos, when identifiable, are typically heavy and do not play an important role in cosmology.

hep-th↗

arXiv2009

A Bound on the Superpotential

We prove a general bound on the superpotential in theories with broken supersymmetry and broken R-symmetry, 2|W|< f_a F, where f_a and F are the R-axion and Goldstino decay constants, respectively. The bound holds for weakly coupled as well as strongly coupled theories, thereby providing an exact result in theories with broken supersymmetry. We briefly discuss several possible applications.

hep-th↗

arXiv2009

Dynamics of the Peccei Quinn Scale

Invoking the Peccei-Quinn (PQ) solution to the strong CP problem substitutes the puzzle of why $θ_{qcd}$ is so small with the puzzle of why the PQ symmetry is of such high quality. Cosmological and astrophysical considerations raise further puzzles. This paper explores this issues in several contexts: string theory and field theory, and theories without and with low energy supersymmetry. Among the questions studied are whether requiring axion dark matter can account for the quality of the PQ symmetry, to which the answer is sometimes yes. In non-supersymmetric theories, we find $f_a = 10^{12}$ GeV is quite plausible. In gauge mediation, cosmological constraints on pseudomoduli place $f_a$ in this range, and require that the gravitino mass be of order an MeV.

hep-th↗

arXiv2009

The Fate of Nearly Supersymmetric Vacua

Supersymmetric vacua are stable. It is interesting to ask: how long-lived are vacua which are nearly supersymmetric? This question is relevant if our universe is approximately supersymmetric. It is also of importance for a number of issues of the physics of the landscape and eternal inflation. In this note, we distinguish a variety of cases. In all of them the decay is slow. For a flat space theory decaying to a deep AdS vacuum, the leading behavior of the decay amplitude, if a thin wall approximation is valid, is ${\cal A} = γe^{-2 π^2/({\rm Re} m_{3/2})^2}$ (where the phase of $m_{3/2}$ is defined in the text) for ${\rm Re} m_{3/2}>0$, and zero otherwise. Metastable supersymmetry breaking generally yields parametrically more rapid decays. For nearly supersymmetric decays, we will see that it is necessary to compute subleading terms in the exponential to extraordinarily high accuracy before one can meaningfully discuss the prefactor.

hep-th↗

arXiv2008

A Bohr-Sommerfeld quantization formula for quasinormal frequencies of AdS black holes

We derive a quantization formula of Bohr-Sommerfeld type for computing quasinormal frequencies for scalar perturbations in an AdS black hole in the limit of large scalar mass or spatial momentum. We then apply the formula to find poles in retarded Green functions of boundary CFTs on $R^{1,d-1}$ and $RxS^{d-1}$. We find that when the boundary theory is perturbed by an operator of dimension $Δ>> 1$, the relaxation time back to equilibrium is given at zero momentum by ${1 \over ΔπT} << {1 \over πT}$. Turning on a large spatial momentum can significantly increase it. For a generic scalar operator in a CFT on $R^{1,d-1}$, there exists a sequence of poles near the lightcone whose imaginary part scales with momentum as $p^{-{d-2 \over d+2}}$ in the large momentum limit. For a CFT on a sphere $S^{d-1}$ we show that the theory possesses a large number of long-lived quasiparticles whose imaginary part is exponentially small in momentum.

gr-qc↗

arXiv2008

Implementing General Gauge Mediation

Recently there has been much progress in building models of gauge mediation, often with predictions different than those of minimal gauge mediation. Meade, Seiberg, and Shih have characterized the most general spectrum which can arise in gauge mediated models. We discuss some of the challenges of building models of General Gauge Mediation, especially the problem of messenger parity and issues connected with R symmetry breaking and CP violation. We build a variety of viable, weakly coupled models which exhibit some or all of the possible low energy parameters.

hep-ph↗

arXiv2007

Metastable Domains of the Landscape

We argue that the vast majority of flux vacua with small cosmological constant are unstable to rapid decay to a big crunch. Exceptions are states with large compactification volume and supersymmetric and approximately supersymmetric states. Neither weak string coupling, warping, or the existence of very light particles are, by themselves, enough to render states reasonably metastable. We speculate, as well, about states which might be cosmological attractors.

hep-th↗

arXiv2007

The arrow of time, black holes, and quantum mixing of large N Yang-Mills theories

Quantum gravity in an AdS spacetime is described by an SU(N) Yang-Mills theory on a sphere, a bounded many-body system. We argue that in the high temperature phase the theory is intrinsically non-perturbative in the large N limit. At any nonzero value of the 't Hooft coupling $λ$, an exponentially large (in N^2) number of free theory states of wide energy range (of order N) mix under the interaction. As a result the planar perturbation theory breaks down. We argue that an arrow of time emerges and the dual string configuration should be interpreted as a stringy black hole.

hep-th↗

arXiv2007

Hagedorn divergences and tachyon potential

We consider the critical behavior for a string theory near the Hagedorn temperature. We use the factorization of the worldsheet to isolate the Hagedorn divergences at all genera. We show that the Hagedorn divergences can be resummed by introducing double scaling limits, which smooth the divergences. The double scaling limits also allow one to extract the effective potential for the thermal scalar. For a string theory in an asymptotic anti-de Sitter (AdS) spacetime, the AdS/CFT correspondence implies that the critical Hagedorn behavior and the relation with the effective potential should also arise from the boundary Yang-Mills theory. We show that this is indeed the case. In particular we find that the free energy of a Yang-Mills theory contains ``vortex'' contributions at finite temperature. Yang-Mills Feynman diagrams with vortices can be identified with contributions from boundaries of moduli space on the string theory side.

hep-th↗

arXiv2005

Inheritance principle and Non-renormalization theorems at finite temperature

We present a general proof of an ``inheritance principle'' satisfied by a weakly coupled SU(N) gauge theory with adjoint matter on a class of compact manifolds (like $S^3$). In the large $N$ limit, finite temperature correlation functions of gauge invariant single-trace operators in the low temperature phase are related to those at zero temperature by summing over images of each operator in the Euclidean time direction. As a consequence, various non-renormalization theorems of $\NN=4$ Super-Yang-Mills theory on $S^3$ survive at finite temperature despite the fact that the conformal and supersymmetries are both broken.

hep-th↗