Deconfinement Transition in Large N Lattice Gauge Theory

TL;DR

This paper analytically investigates the phase diagram and deconfinement transition in large N lattice gauge theories, connecting two-dimensional QCD phase transitions with higher-dimensional deconfinement, and validating results with simulations.

Contribution

It introduces an analytical approach using large N techniques to study the deconfinement transition in lattice gauge theories, linking it to the Douglas-Kazakov transition and matching simulation data.

Findings

Analytic estimates of critical deconfinement temperature agree with simulations.

Established a connection between 2D QCD phase transition and higher-dimensional deconfinement.

Applied large N techniques to both Wilson and Heat Kernel actions in different coupling regimes.

Abstract

We study analytically the phase diagram of the pure $SU(N)$ lattice gauge theory at finite temperature, and we attempt to estimate the critical deconfinement temperature. We apply large $N$ techniques to the Wilson and to the Heat Kernel action, and we study the resulting models both in the strong coupling and in the weak coupling limits. Using the Heat Kernel action, we establish an interesting connection between the Douglas-Kazakov phase transition of two-dimensional QCD and the deconfining transition in $d$ dimensions. The analytic results obtained for the critical temperature compare well with Montecarlo simulations of the full theory in $(2+1)$ and in $(3+1)$ dimensions.