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

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.

arXiv commentv1: 11 pages with 5 figures and data release at https://zenodo.org/record/4059477

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• Non-perturbative phase structure of the bosonic BMN matrix model