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

## TL;DR

This paper investigates the phase structure of super-Yang-Mills theory on a circle at strong coupling, revealing a first-order phase transition between uniform and localized states, and compares gravitational results with lattice computations.

## Contribution

It constructs and analyzes thermal states in the gravity dual of super-Yang-Mills theory on a circle, providing the first test of a first-order phase transition in gauge/gravity duality with lattice data.

## Key findings

- Identifies a first-order phase transition between uniform and localized states.
- Provides critical values for the phase transition.
- First comparison of lattice and gravity results for this transition.

## Abstract

At low energies or temperatures, maximally supersymmetric Yang-Mills theory on $\mathbb R^{(t)}\times S^1$ 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 $S^1$ 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.