Notes on ten-dimensional localized black holes and deconfined states in two-dimensional SYM

TL;DR

This paper numerically constructs ten-dimensional localized black holes with a compact dimension, analyzes their critical behavior, and relates these solutions to the phase structure of two-dimensional super Yang-Mills theory, providing precise phase transition data.

Contribution

It provides the first numerical construction of ten-dimensional localized black holes and links these solutions to the phase diagram of 2D super Yang-Mills theory, including accurate phase transition details.

Findings

Critical behavior follows a logarithmic scaling predicted by double-cone metric.

Localized black hole solutions correspond to the deconfined phase in 2D SYM.

Precise determination of the confinement/deconfinement transition and latent heat.

Abstract

We numerically construct static localized black holes in ten spacetime dimensions with one compact periodic dimension. In particular, we investigate the critical regime in which the poles of the localized black hole are about to merge. When approaching the critical region, the behavior of physical quantities is described by a single real valued exponent giving rise to a logarithmic scaling of the thermodynamic quantities, in agreement with the theoretical prediction derived from the double-cone metric. As a peculiarity, the localized black hole solution in ten dimensions can be related to the spatially deconfined phase of two dimensional N=(8,8) super Yang-Mills theory (SYM) on a spatial circle. We use the localized black hole solutions to determine the SYM phase diagram. In particular, we compute the location of the first order phase confinement/deconfinement transition and the related latent heat to unprecedented accuracy.