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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 thedecoupling limit of a stack of $N$ D$2$-branes, which may be described by IIAsupergravity.We study this conjecture in the Euclidean setting usingnonperturbative lattice gauge theory calculations.Our supersymmetric latticeconstruction naturally puts the theory on a skewed Euclidean 3-torus. Takingone cycle to have anti-periodic fermion boundary conditions, the large-toruslimit is described by certain Euclidean black holes. We compute the bosonicaction---the variation of the partition function---and compare our numericalresults 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 withthe expected gravity behavior in the appropriate large-torus limit.

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