Superconformal indices of three-dimensional theories related by mirror symmetry

Krattenthaler, C.; Spiridonov, V. P.; Vartanov, G. S.

doi:10.1007/JHEP06(2011)008

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Superconformal indices of three-dimensional theories related by mirror symmetry

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Vartanov, G. S.
Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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1103.4075
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1103.4075v2.pdf
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JHEP2011_008.pdf
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Krattenthaler, C., Spiridonov, V. P., & Vartanov, G. S. (2011). Superconformal indices of three-dimensional theories related by mirror symmetry. Journal of High Energy Physics, 2011: 008. doi:10.1007/JHEP06(2011)008.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0011-3030-9

Abstract

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 the mirror symmetry. The proofs are based on the well known identities of the theory of $q$-special functions. We also suggest the general index formula taking into account the $U(1)_J$ global symmetry present for abelian theories.