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Ofer Aharony

Publications and source records attributed to Ofer Aharony.

At least 91 records · Page 5Linked to original sources
arXiv2007

The black hole in the throat - thermodynamics of strongly coupled cascading gauge theories

We numerically construct black hole solutions corresponding to the deconfined, chirally symmetric phase of strongly coupled cascading gauge theories at various temperatures. We compute the free energy as a function of the temperature, and we show that it becomes positive below some critical temperature, indicating the possibility of a first order phase transition at which the theory deconfines and restores the chiral symmetry.

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arXiv2007

Stringy Instantons and Cascading Quivers

D-brane instantons can perturb the quantum field theories on space-time filling D-branes by interesting operators. In some cases, these D-brane instantons are novel "stringy" effects (not interpretable directly as instanton effects in the low-energy quantum field theory), while in others the D-brane instantons can be directly interpreted as field theory effects. In this note, we describe a situation where both perspectives are available, by studying stringy instantons in quivers which arise at simple Calabi-Yau singularities. We show that a stringy instanton which wraps an unoccupied node of the quiver, and gives rise to a non-perturbative mass in the space-time field theory, can be reinterpreted as a conventional gauge theory effect by going up in an appropriate renormalization group cascade. Interestingly, in the cascade, the contribution of the stringy instanton does not come from gauge theory instantons but from strong coupling dynamics.

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arXiv2007

A phase transition in commuting Gaussian multi-matrix models

We analyze in detail a second order phase transition that occurs in large N Gaussian multi-matrix models in which the matrices are constrained to be commuting. The phase transition occurs as the relative masses of the matrices are varied, assuming that there are at least four matrices in the lowest mass level. We also discuss the phase structure of weakly coupled large N 3+1 dimensional gauge theories compactified on a three-sphere of radius R. We argue that these theories are well described at high temperatures (T >> 1/R) by a Gaussian multi-matrix model, and that they do not exhibit any phase transitions between the deconfinement scale (T ~ 1/R) and the scale where perturbation theory breaks down (T ~ 1 / λR, where λis the 't Hooft coupling).

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arXiv2007

The Moduli Space and M(atrix) Theory of 9d N=1 Backgrounds of M/String Theory

We discuss the moduli space of nine dimensional N=1 supersymmetric compactifications of M theory / string theory with reduced rank (rank 10 or rank 2), exhibiting how all the different theories (including M theory compactified on a Klein bottle and on a Mobius strip, the Dabholkar-Park background, CHL strings and asymmetric orbifolds of type II strings on a circle) fit together, and what are the weakly coupled descriptions in different regions of the moduli space. We argue that there are two disconnected components in the moduli space of theories with rank 2. We analyze in detail the limits of the M theory compactifications on a Klein bottle and on a Mobius strip which naively give type IIA string theory with an uncharged orientifold 8-plane carrying discrete RR flux. In order to consistently describe these limits we conjecture that this orientifold non-perturbatively splits into a D8-brane and an orientifold plane of charge (-1) which sits at infinite coupling. We construct the M(atrix) theory for M theory on a Klein bottle (and the theories related to it), which is given by a 2+1 dimensional gauge theory with a varying gauge coupling compactified on a cylinder with specific boundary conditions. We also clarify the construction of the M(atrix) theory for backgrounds of rank 18, including the heterotic string on a circle.

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arXiv2007

Supercritical stability, transitions and (pseudo)tachyons

Highly supercritical strings (c much greater than 15) with a time-like linear dilaton provide a large class of solutions to string theory, in which closed string tachyon condensation is under control (and follows the worldsheet renormalization group flow). In this note we analyze the late-time stability of such backgrounds, including transitions between them. The large friction introduced by the rolling dilaton and the rapid decrease of the string coupling suppress the back-reaction of naive instabilities. In particular, although the graviton, dilaton, and other light fields have negative effective mass squared in the linear dilaton background, the decaying string coupling ensures that their condensation does not cause large back-reaction. Similarly, the copious particles produced in transitions between highly supercritical theories do not back-react significantly on the solution. We discuss these features also in a somewhat more general class of time-dependent backgrounds with stable late-time asymptotics.

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arXiv2007

Comments on worldsheet theories dual to free large N gauge theories

We continue to investigate properties of the worldsheet conformal field theories (CFTs) which are conjectured to be dual to free large N gauge theories, using the mapping of Feynman diagrams to the worldsheet suggested in hep-th/0504229. The modular invariance of these CFTs is shown to be built into the formalism. We show that correlation functions in these CFTs which are localized on subspaces of the moduli space may be interpreted as delta-function distributions, and that this can be consistent with a local worldsheet description given some constraints on the operator product expansion coefficients. We illustrate these features by a detailed analysis of a specific four-point function diagram. To reliably compute this correlator we use a novel perturbation scheme which involves an expansion in the large dimension of some operators.

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arXiv2006

Short distance properties of cascading gauge theories

We study the short distance (large momentum) properties of correlation functions of cascading gauge theories by performing a tree-level computation in their dual gravitational background. We prove that these theories are holographically renormalizable; the correlators have only analytic ultraviolet divergences, which may be removed by appropriate local counterterms. We find that n-point correlation functions of properly normalized operators have the expected scaling in the semi-classical gravity (large N) limit: they scale as N_{eff}^{2-n} with N_{eff} proportional to ln(k/Lambda) where k is a typical momentum. Our analysis thus confirms the interpretation of the cascading gauge theories as renormalizable four-dimensional quantum field theories with an effective number of degrees of freedom which logarithmically increases with the energy.

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arXiv2006

The CFT/AdS correspondence, massive gravitons and a connectivity index conjecture

We discuss the general question of which conformal field theories have dual descriptions in terms of quantum gravity theories on anti-de Sitter space. We analyze in detail the case of a deformed product of n conformal field theories (each of which has a gravity dual), and we claim that the dual description of this is by a quantum gravity theory on a union of n anti-de Sitter spaces, connected at their boundary (by correlations between their boundary conditions). On this union of spaces, (n-1) linear combinations of gravitons obtain a mass, and we compute this mass both from the field theory and from the gravity sides of the correspondence, finding the same result in both computations. This is the first example in which a graviton mass in the bulk of anti-de Sitter space arises continuously by varying parameters. The analysis of these deformed product theories leads us to suggest that field theories may be generally classified by a "connectivity index", corresponding to the number of components (connected at the boundary) in the space-time of the dual gravitational background. In the field theory this index roughly counts the number of independent gauge groups, but we do not have a precise general formula for the index.

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arXiv2006

Two loop partition function for large N pure Yang-Mills theory on a small three-sphere

We give a direct path-integral calculation of the partition function for pure 3+1 dimensional U(N) Yang-Mills theory at large N on a small three-sphere, up to two-loop order in perturbation theory. From this, we calculate the one-loop shift in the Hagedorn/deconfinement temperature for the theory at small volume, finding that it increases (in units of the inverse sphere radius) as we go to larger coupling (larger volume). Our results also allow us to read off the sum of one-loop anomalous dimensions for all operators with a given engineering dimension in planar Yang-Mills theory on R^4. As checks on our calculation, we reproduce both the Hagedorn shift and some of the anomalous dimension sums by independent methods using the results of hep-th/0412029 and hep-th/0408178. The success of our calculation provides a significant check of methods used in hep-th/0502149 to establish a first order deconfinement transition for pure Yang-Mills theory on a small three-sphere.

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arXiv2006

A first order deconfinement transition in large N Yang-Mills theory on a small 3-sphere

We give an analytic demonstration that the 3+1 dimensional large N SU(N) pure Yang-Mills theory, compactified on a small 3-sphere so that the coupling constant at the compactification scale is very small, has a first order deconfinement transition as a function of temperature. We do this by explicitly computing the relevant terms in the canonical partition function up to 3-loop order; this is necessary because the leading (1-loop) result for the phase transition is precisely on the borderline between a first order and a second order transition. Since numerical work strongly suggests that the infinite volume large N theory also has a first order deconfinement transition, we conjecture that the phase structure is independent of the size of the 3-sphere. To deal with divergences in our calculations, we are led to introduce a novel method of regularization useful for nonabelian gauge theory on a 3-sphere.

hep-th↗
arXiv2006

A holographic model of deconfinement and chiral symmetry restoration

We analyze the finite temperature behavior of the Sakai-Sugimoto model, which is a holographic dual of a theory which spontaneously breaks a U(N_f)_L x U(N_f)_R chiral flavor symmetry at zero temperature. The theory involved is a 4+1 dimensional supersymmetric SU(N_c) gauge theory compactified on a circle of radius R with anti-periodic boundary conditions for fermions, coupled to N_f left-handed quarks and N_f right-handed quarks which are localized at different points on the compact circle (separated by a distance L). In the supergravity limit which we analyze (corresponding in particular to the large N_c limit of the gauge theory), the theory undergoes a deconfinement phase transition at a temperature T_d = 1 / 2 πR. For quark separations obeying L > L_c = 0.97 * R the chiral symmetry is restored at this temperature, but for L < L_c = 0.97 * R there is an intermediate phase which is deconfined with broken chiral symmetry, and the chiral symmetry is restored at T = 0.154 / L. All of these phase transitions are of first order.

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arXiv2006

On the worldsheet theories of strings dual to free large N gauge theories

We analyze in detail some properties of the worldsheet of the closed string theories suggested by Gopakumar to be dual to free large N SU(N) gauge theories (with adjoint matter fields). We use Gopakumar's prescription to translate the computation of space-time correlation functions to worldsheet correlation functions for several classes of Feynman diagrams, by explicit computations of Strebel differentials. We compute the worldsheet operator product expansion in several cases and find that it is consistent with general worldsheet conformal field theory expectations. A peculiar property of the construction is that in several cases the resulting worldsheet correlation functions are non-vanishing only on a sub-space of the moduli space (say, for specific relations between vertex positions). Another strange property we find is that for a conformally invariant space-time theory, the mapping to the worldsheet does not preserve the special conformal symmetries, so that the full conformal group is not realized as a global symmetry on the worldsheet (even though it is, by construction, a symmetry of all integrated correlation functions).

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arXiv2006

The Phase Structure of Low Dimensional Large N Gauge Theories on Tori

In this paper we continue our study of the thermodynamics of large N gauge theories on compact spaces. We consider toroidal compactifications of pure SU(N) Yang-Mills theories and of maximally supersymmetric Yang-Mills theories dimensionally reduced to 0+1 or 1+1 dimensions, and generalizations of such theories where the adjoint fields are massive. We describe the phase structure of these theories as a function of the gauge coupling, the geometry of the compact space and the mass parameters. In particular, we study the behavior of order parameters associated with the holonomy of the gauge field around the cycles of the torus. Our methods combine analytic analysis, numerical Monte Carlo simulations, and (in the maximally supersymmetric case) information from the dual gravitational theories.

hep-th↗
arXiv2005

Plasma-balls in large N gauge theories and localized black holes

We argue for the existence of plasma-balls - meta-stable, nearly homogeneous lumps of gluon plasma at just above the deconfinement energy density - in a class of large N confining gauge theories that undergo first order deconfinement transitions. Plasma-balls decay over a time scale of order N^2 by thermally radiating hadrons at the deconfinement temperature. In gauge theories that have a dual description that is well approximated by a theory of gravity in a warped geometry, we propose that plasma-balls map to a family of classically stable finite energy black holes localized in the IR. We present a conjecture for the qualitative nature of large mass black holes in such backgrounds, and numerically construct these black holes in a particular class of warped geometries. These black holes have novel properties; in particular their temperature approaches a nonzero constant value at large mass. Black holes dual to plasma-balls shrink as they decay by Hawking radiation; towards the end of this process they resemble ten dimensional Schwarzschild black holes, which we propose are dual to small plasma-balls. Our work may find practical applications in the study of the physics of localized black holes from a dual viewpoint.

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arXiv2005

The Conformal Limit of the 0A Matrix Model and String Theory on AdS(2)

We analyze the conformal limit of the matrix model describing flux backgrounds of two dimensional type 0A string theory. This limit is believed to be dual to an AdS(2) background of type 0A string theory. We show that the spectrum of this limit is identical to that of a free fermion on AdS(2), suggesting that there are no closed string excitations in this background.

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arXiv2005

Non-Local Effects of Multi-Trace Deformations in the AdS/CFT Correspondence

The AdS/CFT correspondence relates deformations of the CFT by "multi-trace operators" to "non-local string theories". The deformed theories seem to have non-local interactions in the compact directions of space-time; in the gravity approximation the deformed theories involve modified boundary conditions on the fields which are explicitly non-local in the compact directions. In this note we exhibit a particular non-local property of the resulting space-time theory. We show that in the usual backgrounds appearing in the AdS/CFT correspondence, the commutator of two bulk scalar fields at points with a large enough distance between them in the compact directions and a small enough time-like distance between them in AdS vanishes, but this is not always true in the deformed theories. We discuss how this is consistent with causality.

hep-th↗
arXiv2005

Holographic renormalization of cascading gauge theories

We perform a holographic renormalization of cascading gauge theories. Specifically, we find the counter-terms that need to be added to the gravitational action of the backgrounds dual to the cascading theory of Klebanov and Tseytlin, compactified on an arbitrary four-manifold, in order to obtain finite correlation functions (with a limited set of sources). We show that it is possible to truncate the action for deformations of this background to a five dimensional system coupling together the metric and four scalar fields. Somewhat surprisingly, despite the fact that these theories involve an infinite number of high-energy degrees of freedom, we find finite answers for all one-point functions (including the conformal anomaly). We compute explicitly the renormalized stress tensor for the cascading gauge theories at high temperature and show how our finite answers are consistent with the infinite number of degrees of freedom. Finally, we discuss ambiguities appearing in the holographic renormalization we propose for the cascading gauge theories; our finite results for the one-point functions have some ambiguities in curved space (including the conformal anomaly) but not in flat space.

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