Monte Carlo Studies of the GWW Phase Transition in Large-N Gauge Theories

TL;DR

This paper demonstrates the existence of a Gross-Witten-Wadia phase transition in a finite-temperature N=4 SYM gauge theory on S^3 using Monte Carlo simulations, linking it to black hole-string transitions in string theory.

Contribution

It provides the first Monte Carlo evidence of the GWW transition in a non-trivial gauge theory, supporting the gauge/gravity duality and the black hole-string transition hypothesis.

Findings

Identification of the GWW transition at critical temperature T_c

Universal fluctuation formulas near the transition

Discussion of SO(6) R-symmetry breaking effects

Abstract

In the study of the small ten-dimensional Schwarzschild blackhole, the blackhole to string transition is an important problem. In hep-th/0605041, a possible identification is made between the Gross-Witten-Wadia (GWW) type third-order large-N phase transition in the boundary gauge theory and the string-black hole transition in the bulk. In this paper, we exhibit the existence of the GWW transition by Monte Carlo simulation in the zero mode bosonic action of the finite-temperature N=4 SYM theory on S^3. Exhibiting this transition in the truncated but highly non-trivial gauge theory implies that in the vicinity of the critical temperature T_c, the system goes critical, and the fluctuations give rise to universal formulas derived in hep-th/0605041 We also discuss the issue of SO(6) R-symmetry breaking.