Three-dimensional super-Yang--Mills theory on the lattice and dual black branes

TL;DR

This paper investigates the duality between three-dimensional maximally supersymmetric SU(N) Yang-Mills theory and black branes using nonperturbative lattice simulations, providing evidence supporting the gauge/gravity correspondence.

Contribution

It presents the first nonperturbative lattice study of 3D super-Yang-Mills theory and compares numerical results with supergravity predictions in the large-torus limit.

Findings

Numerical results agree with supergravity predictions in the large-torus limit.

Lattice construction effectively captures supersymmetric gauge theory dynamics.

Results support the gauge/gravity duality in the studied regime.

Abstract

In the large-$N$ and strong-coupling limit, maximally supersymmetric SU($N$) Yang--Mills theory in $(2 + 1)$ dimensions is conjectured to be dual to the decoupling limit of a stack of $N$ D$2$-branes, which may be described by IIA supergravity.We study this conjecture in the Euclidean setting using nonperturbative lattice gauge theory calculations.Our supersymmetric lattice construction naturally puts the theory on a skewed Euclidean 3-torus. Taking one cycle to have anti-periodic fermion boundary conditions, the large-torus limit is described by certain Euclidean black holes. We compute the bosonic action---the variation of the partition function---and compare our numerical results to the supergravity prediction as the size of the torus is changed, keeping its shape fixed. Our lattice calculations primarily utilize $N = 8$ with extrapolations to the continuum limit, and our results are consistent with the expected gravity behavior in the appropriate large-torus limit.