Phases of a two dimensional large N gauge theory on a torus

Abstract

We consider two-dimensional large N gauge theory with D adjoint scalars on a torus, which is obtained from a D+2 dimensional pure Yang-Mills theory on T^{D+2} with D small radii. The two dimensional model has various phases characterized by the holonomy of the gauge field around non-contractible cycles of the 2-torus. We determine the phase boundaries and derive the order of the phase transitions using a method, developed in an earlier work (arxiv:0910.4526), which is nonperturbative in the 'tHooft coupling and uses a 1/D expansion. We embed our phase diagram in the more extensive phase structure of the D+2 dimensional Yang-Mills theory and match with the picture of a cascade of phase transitions found earlier in lattice calculations (arxiv:0710.0098). We also propose a dual gravity system based on a Scherk-Schwarz compactification of a D2 brane wrapped on a 3-torus and find a phase structure which is similar to the phase diagram found in the gauge theory calculation.

28 pages (+ 17 pages of appendix + 6 pages of ref.); 8 figures; (v2) LaTeX Showkeys command deleted; (v3) refs and minor clarifications added; emphasized the new proposal for applying holography to nonsupersymmetric gauge theory; (v4) modified the arguments about holography; (v5) minor corrections, version appeared in PRD

References in corpus (11)

• A holographic model of deconfinement and chiral symmetry restoration
• Instabilities of Black Strings and Branes
• Gregory-Laflamme as the confinement/deconfinement transition in holographic QCD
• Continuum Thermodynamics of the GluoN_c Plasma
• Phase structure of matrix quantum mechanics at finite temperature
• Lattice study of two-dimensional N=(2,2) super Yang-Mills at large-N
• Large-N reduction in QCD-like theories with massive adjoint fermions
• On the shape of a D-brane bound state and its topology change
• Cascade of Gregory-Laflamme Transitions and U(1) Breakdown in Super Yang-Mills
• Phases of three dimensional large N QCD on a continuum torus
• Monte Carlo Studies of the GWW Phase Transition in Large-N Gauge Theories

Cited by in corpus (15)

• The BFSS model on the lattice
• Gregory-Laflamme as the confinement/deconfinement transition in holographic QCD
• Testing holography using lattice super-Yang--Mills on a 2-torus
• Quantum quench in matrix models: Dynamical phase transitions, Selective equilibration and the Generalized Gibbs Ensemble
• What is the gravity dual of the confinement/deconfinement transition in holographic QCD?
• Finite-temperature phase transitions of third and higher order in gauge theories at large $N$
• Critical Dimension and Negative Specific Heat in One-dimensional Large-N Reduced Models
• New States of Gauge Theories on a Circle
• Real Time Quantum Gravity Dynamics from Classical Statistical Yang-Mills Simulations
• Two approaches to quantum gravity and M-(atrix) theory at large number of dimensions
• A Scaling Relation, $Z_m$-type Deconfinement Phases and Imaginary Chemical Potentials in Finite Temperature Large-$N$ Gauge Theories
• D-dependence of gap between critical temperatures in one-dimensional gauge theories
• Moduli dynamics as a predictive tool for thermal maximally supersymmetric Yang-Mills at large N
• Novel first-order phase transition and critical points in SU(3) Yang-Mills theory with spatial compactification
• Membrane Matrix models and non-perturbative checks of gauge/gravity duality