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Superconformal indices of three-dimensional theories related by mirror symmetry. (English) Zbl 1298.81186

Summary: Recently, Kim, and Imamura and Yokoyama derived an exact formula for superconformal indices in three-dimensional field theories. Using their results, we prove analytically the equality of superconformal indices in some U(1)-gauge group theories related by mirror symmetry. The proofs are based on well-known identities in the theory of \(q\)-special functions. We also suggest a general index formula taking into account the U(1)\({}_{J}\) global symmetry present for abelian theories.

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
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