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High Energy Physics - Theory, hep-th
Abstract:
An exact formula for partition functions in 3d field theories was recently
suggested by Jafferis, and Hama, Hosomichi, and Lee. These functions are
expressed in terms of specific $q$-hypergeometric integrals whose key building
block is the double sine function (or the hyperbolic gamma function). Elliptic
hypergeometric integrals, discovered by the second author, define 4d
superconformal indices. Using their reduction to the hyperbolic level, we
describe a general scheme of reducing 4d superconformal indices to 3d partition
functions. As an example, we consider explicitly the duality pattern for 3d
$\mathcal{N}=2$ SYM and CS theories with SP(2N) gauge group with adjoint
matter.
