Monte Carlo studies of the GWW phase transition in large-N gauge theories

Abstract

In the study of the small ten-dimensional Schwarzschild black hole, the black hole to string transition is an important problem. In [L. Alvarez-Gaumé, P. Basu, M. Marino, S.R. Wadia, Eur. Phys. J. C 48 (2006) 647 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 Letter, 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 S³. 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 [L. Alvarez-Gaumé, P. Basu, M. Marino, S.R. Wadia, Eur. Phys. J. C 48 (2006) 647, hep-th/0605041]. We also discuss the issue of SO(6) R-symmetry breaking.