Gauge theory duals of black hole – black string transitions of gravitational theories on a circle (original) (raw)
Related papers
Classical and Quantum Gravity, 2004
We review and extend earlier work that uses the AdS/CFT correspondence to relate the black hole-black string transition of gravitational theories on a circle to a phase transition in maximally supersymmetric 1 + 1 dimensional SU (N) gauge theories at large N , again compactified on a circle. We perform gravity calculations to determine a likely phase diagram for the strongly coupled gauge theory. We then directly study the phase structure of the same gauge theory, now at weak 't Hooft coupling. In the interesting temperature regime for the phase transition, the 1+1 dimensional theory reduces to a 0 + 1 dimensional bosonic theory, which we solve using Monte Carlo methods. We find strong evidence that the weakly coupled gauge theory also exhibits a black hole-black string like phase transition in the large N limit. We demonstrate that a simple Landau-Ginzburg like model describes the behaviour near the phase transition remarkably well. The weak coupling transition appears to be close to the cusp between a first order and a second order transition.
Thermal phases of D1-branes on a circle from lattice super Yang-Mills
Journal of High Energy Physics, 2010
We report on the results of numerical simulations of 1 + 1 dimensional SU (N ) Yang-Mills theory with maximal supersymmetry at finite temperature and compactified on a circle. For large N this system is thought to provide a dual description of the decoupling limit of N coincident D1-branes on a circle. It has been proposed that at large N there is a phase transition at strong coupling related to the Gregory-Laflamme (GL) phase transition in the holographic gravity dual. In a high temperature limit there was argued to be a deconfinement transition associated to the spatial Polyakov loop, and it has been proposed that this is the continuation of the strong coupling GL transition. Investigating the theory on the lattice for SU (3) and SU (4) and studying the time and space Polyakov loops we find evidence supporting this. In particular at strong coupling we see the transition has the parametric dependence on coupling predicted by gravity. We estimate the GL phase transition temperature from the lattice data which, interestingly, is not yet known directly in the gravity dual. Fine tuning in the lattice theory is avoided by the use of a lattice action with exact supersymmetry.
Towards lattice simulation of the gauge theory duals to black holes and hot strings
Journal of High Energy Physics, 2007
A generalization of the AdS/CFT conjecture postulates a duality between IIA string theory and 16 supercharge Yang-Mills quantum mechanics in the large N 't Hooft limit. At low temperatures string theory describes black holes, whose thermodynamics may hence be studied using the dual quantum mechanics. This quantum mechanics is strongly coupled which motivates the use of lattice techniques. We argue that, contrary to expectation, the theory when discretized naively will nevertheless recover continuum supersymmetry as the lattice spacing is sent to zero. We test these ideas by studying the 4 supercharge version of this Yang-Mills quantum mechanics in the 't Hooft limit. We use both a naive lattice action and a manifestly supersymmetric action. Using Monte Carlo methods we simulate the Euclidean theories, and study the lattice continuum limit, for both thermal and non-thermal periodic boundary conditions, confirming continuum supersymmetry is recovered for the naive action when appropriate. We obtain results for the thermal system with N up to 12. These favor the existence of a single deconfined phase for all non-zero temperatures. These results are an encouraging indication that the 16 supercharge theory is within reach using similar methods and resources.
The properties of D1-branes from lattice super Yang–Mills theory using gauge/gravity duality
The two-dimensional supersymmetric Yang-Mills (SYM) theory with sixteen supercharges at large N and strong 't Hooft coupling is conjectured to be dual to certain supergravity solutions in the decoupling limit. We discretize the gauge theory preserving a subset of supersymmetries on the lattice. Based on the choice of a point in the moduli space for the expansion of the gauge links to target the correct continuum theory, one ends up with different lattice geometries. In our previous work, we explored the free energy and the phase structure on a skewed torus corresponding to A2* lattice geometry. Here, we will consider square lattice and calculate the free energy, equation of state and speed of sound in this strongly coupled supersymmetric plasma. Since there is no shear viscosity in two dimensions, we comment on the expectations for the bulk viscosity from the calculations on the dual supergravity side, which unlike the conformal N = 4 SYM case does not vanish and is proportional to the trace of energy-momentum tensor.
Gauge-gravity duality--Super Yang Mills Quantum Mechanics
Arxiv preprint arXiv:0709.3497, 2007
We describe the conjectured holographic duality between Yang-Mills quantum mechanics and type IIa string theory. This duality allows us to use lattice Monte Carlo simulations to probe the physics of the gravitational theory - for example, at low energies it provides a computation ...
Extracting black hole physics from the lattice
Journal of High Energy Physics, 2010
We perform lattice simulations of N D0-branes at finite temperature in the decoupling limit, namely 16 supercharge SU (N ) Yang-Mills quantum mechanics in the 't Hooft limit. At low temperature this theory is conjectured to be dual to certain supergravity black holes. We emphasize that the existence of a non-compact moduli space renders the partition function of the quantum mechanics theory divergent, and we perform one loop calculations that demonstrate this explicitly. In consequence we use a scalar mass term to regulate this divergence and argue that the dual black hole thermodynamics may be recovered in the appropriate large N limit as the regulator is removed. We report on simulations for N up to 5 including the Pfaffian phase, and N up to 12 in the phase quenched approximation. Interestingly, in the former case, where we may calculate this potentially difficult phase, we find that it appears to play little role dynamically over the temperature range tested, which is certainly encouraging for future simulations of this theory.
Black hole thermodynamics from simulations of lattice Yang-Mills theory
Physical Review D, 2008
We report on lattice simulations of 16 supercharge SU (N ) Yang-Mills quantum mechanics in the 't Hooft limit. Maldacena duality conjectures that in this limit the theory is dual to IIA string theory, and in particular that the behavior of the thermal theory at low temperature is equivalent to that of certain black holes in IIA supergravity. Our simulations probe the low temperature regime for N ≤ 5 and the intermediate and high temperature regimes for N ≤ 12. We observe 't Hooft scaling and at low temperatures our results are consistent with the dual black hole prediction. The intermediate temperature range is dual to the Horowitz-Polchinski correspondence region, and our results are consistent with smooth behavior there. We include the Pfaffian phase arising from the fermions in our calculations where appropriate.
Testing holography using lattice super-Yang–Mills on a 2-torus
We consider maximally supersymmetric SU(N) Yang–Mills theory in Eu-clidean signature compactified on a flat two-dimensional torus with anti-periodic ('thermal') fermion boundary conditions imposed on one cycle. At large N , holography predicts that this theory describes certain black hole solutions in Type IIA and IIB supergravity, and we use lattice gauge theory to test this. Unlike the one-dimensional quantum mechanics case where there is only the dimensionless temperature to vary, here we emphasize there are two more parameters which determine the shape of the flat torus. While a rectangular Euclidean torus yields a thermal interpretation, allowing for skewed tori modifies the holographic dual black hole predictions and results in another direction to test holography. Our lattice calculations are based on a supersymmetric formulation naturally adapted to a particular skewing. Using this we perform simulations up to N = 16 with several lattice spacings for both skewed and rectangular tori. We observe the two expected black hole phases with their predicted behavior, with a transition between them that is consistent with the gravity prediction based on the Gregory–Laflamme transition.
Large N 2D Yang-Mills Theory and Topological String Theory
Communications in Mathematical Physics, 1997
We describe a topological string theory which reproduces many aspects of the 1/N expansion of SU (N) Yang-Mills theory in two spacetime dimensions in the zero coupling (A = 0) limit. The string theory is a modified version of topological gravity coupled to a topological sigma model with spacetime as target. The derivation of the string theory relies on a new interpretation of Gross and Taylor's "Ω −1 points." We describe how inclusion of the area, coupling of chiral sectors, and Wilson loop expectation values can be incorporated in the topological string approach.
The deconfinement and Hagedorn phase transitions in weakly coupled large N gauge theories
Comptes Rendus Physique, 2004
We demonstrate that weakly coupled, large N , d-dimensional SU (N) gauge theories on a class of compact spatial manifolds (including S d−1 × time) undergo deconfinement phase transitions at temperatures proportional to the inverse length scale of the manifold in question. The low temperature phase has a free energy of order one, and is characterized by a stringy (Hagedorn) growth in its density of states. The high temperature phase has a free energy of order N 2. These phases are separated either by a single first order transition that generically occurs below the Hagedorn temperature or by two continuous phase transitions, the first of which occurs at the Hagedorn temperature. These phase transitions could perhaps be continuously connected to the usual flat space deconfinement transition in the case of confining gauge theories, and to the Hawking-Page nucleation of AdS 5 black holes in the case of the N = 4 supersymmetric Yang-Mills theory. We suggest that deconfinement transitions may generally be interpreted in terms of black hole formation in a dual string theory. Our analysis proceeds by first reducing the Yang-Mills partition function to a (0 + 0)-dimensional integral over a unitary matrix U , which is the holonomy (Wilson loop) of the gauge field around the thermal time circle in Euclidean space; deconfinement transitions are large N transitions in this matrix integral.