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

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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 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 [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. © 2007 Elsevier B.V. All rights reserved.

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Azuma, T., Basu, P., & Wadia, S. R. (2008). Monte Carlo studies of the GWW phase transition in large-N gauge theories. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 659(3), 676–682. https://doi.org/10.1016/j.physletb.2007.11.088

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