New States of Gauge Theories on a Circle

Abstract

We study a one-dimensional large-N U(N) gauge theory on a circle as a toy model of higher dimensional Yang-Mills theories at finite temperature. To investigate the profile of the thermodynamical potential in this model, we evaluate a stochastic time evolution of several states, and find that an unstable confinement phase at high temperature does not decay to a stable deconfinement phase directly. Before it reaches the deconfinement phase, it develops to several intermediate states. These states are characterised by the expectation values of the Polyakov loop operators, which wind the temporal circle different times. We reveal that these intermediate states are the saddle point solutions of the theory, and similar solutions exist in a wide class of SU(N) and U(N) gauge theories on S^1 including QCD and pure Yang-Mills theories in various dimensions. We also consider a Kaluza-Klein gravity, which is the gravity dual of the one-dimensional gauge theory on a spatial S^1, and show that these solutions may be related to multi black holes localised on the S^1. Then we present a connection between the stochastic time evolution of the gauge theory and the dynamical decay process of a black string though the Gregory-Laflamme instability.

34 pages, 10 figures, related movies are on http://www2.yukawa.kyoto-u.ac.jp/~azuma/multi_cut/index.html; v2: minor corrections; v3: minor corrections, to appear in JHEP

References in corpus (9)

• Nonlinear Fluid Dynamics from Gravity
• Black Strings, Low Viscosity Fluids, and Violation of Cosmic Censorship
• Stability of Black Holes and Black Branes
• Blackhole/String Transition for the Small Schwarzschild Blackhole of $Ad{S}_5\times S^5$ and Critical Unitary Matrix Models
• Gregory-Laflamme as the confinement/deconfinement transition in holographic QCD
• Phase structure of matrix quantum mechanics at finite temperature
• Fine structure of Hagedorn transitions
• Phases of a two dimensional large N gauge theory on a torus
• Exact fuzzy sphere thermodynamics in matrix quantum mechanics

Cited by in corpus (8)

• Hagedorn Instability in Dimensionally Reduced Large-N Gauge Theories as Gregory-Laflamme and Rayleigh-Plateau Instabilities
• Quantum quench in matrix models: Dynamical phase transitions, Selective equilibration and the Generalized Gibbs Ensemble
• Spectral form factor for free large $N$ gauge theory and strings
• Instanton dynamics in finite temperature QCD via holography
• A Scaling Relation, $Z_m$-type Deconfinement Phases and Imaginary Chemical Potentials in Finite Temperature Large-$N$ Gauge Theories
• Complex Langevin Method on Rotating Matrix Quantum Mechanics at Thermal Equilibrium
• D-dependence of gap between critical temperatures in one-dimensional gauge theories
• Phase Transitions of a (Super) Quantum Mechanical Matrix Model with a Chemical Potential