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

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 D2-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 antiperiodic 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.