Localised and nonuniform thermal states of super-Yang-Mills on a circle

At low energies or temperatures, maximally supersymmetric Yang-Mills theory on ℝt×S1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathbb{R}}^{(t)}\times {S}^1 $$\end{document} with large N gauge group SU(N ) and strong t’Hooft coupling is conjectured to be dual to the low energy dynamics of a collection of D0-branes on a circle. We construct thermal states in the gravitational side of the correspondence where we find a first-order phase transition between states that are uniform on the S1 and states that are localised on it. When compared with lattice computations that are now available, these critical values provide the first instance where a first-order phase transition is tested on both sides of gauge/gravity duality.