Papers › Three-dimensional super-Yang--Mills theory on the lattice and dual black branes
Three-dimensional super-Yang--Mills theory on the lattice and dual black branes
Simon Catterall, Joel Giedt, Raghav G. Jha, David Schaich, Toby Wiseman
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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 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.
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