New States of Gauge Theories on a Circle

TL;DR

This paper investigates the phase structure of a one-dimensional large-N gauge theory on a circle, revealing intermediate saddle point states and their relation to black hole solutions via gravity duality.

Contribution

It identifies and characterizes intermediate saddle point states in the gauge theory and connects them to multi black hole solutions in gravity duals.

Findings

Unstable confinement phase develops into intermediate states before deconfinement.

Intermediate states are saddle points characterized by Polyakov loop winding numbers.

These states relate to multi black hole configurations in gravity duals.

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.