Thermal phases of D1-branes on a circle from lattice super Yang-Mills

TL;DR

This paper uses lattice simulations of 1+1D supersymmetric Yang-Mills theory to investigate thermal phase transitions related to D1-branes and holographic duality, providing numerical evidence for the Gregory-Laflamme transition.

Contribution

It presents the first lattice simulation evidence supporting the holographic Gregory-Laflamme phase transition in supersymmetric Yang-Mills theory.

Findings

Evidence of phase transition consistent with gravity predictions

Transition temperature estimated from lattice data

Supports the holographic duality between gauge theory and gravity

Abstract

We report on the results of numerical simulations of 1+1 dimensional SU(N) Yang-Mills theory with maximal supersymmetry at finite temperature and compactified on a circle. For large N this system is thought to provide a dual description of the decoupling limit of N coincident D1-branes on a circle. It has been proposed that at large N there is a phase transition at strong coupling related to the Gregory-Laflamme (GL) phase transition in the holographic gravity dual. In a high temperature limit there was argued to be a deconfinement transition associated to the spatial Polyakov loop, and it has been proposed that this is the continuation of the strong coupling GL transition. Investigating the theory on the lattice for SU(3) and SU(4) and studying the time and space Polyakov loops we find evidence supporting this. In particular at strong coupling we see the transition has the parametric dependence on coupling predicted by gravity. We estimate the GL phase transition temperature from the lattice data which, interestingly, is not yet known directly in the gravity dual. Fine tuning in the lattice theory is avoided by the use of a lattice action with exact supersymmetry.