Maximally supersymmetric Yang--Mills in three dimensions

TL;DR

This paper investigates the non-perturbative phase diagram of maximally supersymmetric Yang--Mills theory in three dimensions using lattice methods that preserve some supersymmetry, focusing on the spatial deconfinement transition and its holographic dual.

Contribution

It provides the first lattice study of the phase transition in 3D maximally supersymmetric Yang--Mills theory, confirming holographic predictions for transition temperatures.

Findings

Transition temperatures match holographic expectations

Lattice formulation preserves a subset of supersymmetry

Results support the gauge/gravity duality in 3D SYM

Abstract

We present the latest results from our ongoing lattice field theory investigations of maximally supersymmetric Yang--Mills theory in three space-time dimensions, focusing on its non-perturbative phase diagram. Exploiting a lattice formulation that preserves a subset of the supersymmetry algebra at non-zero lattice spacing, we study the 'spatial deconfinement' phase transition that holography relates to the transition between localized and homogeneous black branes in the dual quantum gravity. Fixing $N_L^2 \times 8$ lattice volumes and N=8 colors in the SU(N) gauge group, we consider four aspect ratios $\alpha = N_L / N_T \leq 4$ corresponding to $N_L = 16$, $20$, $24$ and $32$. The transition temperatures we determine are in good agreement with the low-temperature, large-N holographic expectation $T_c \propto \alpha^3$.