Superconformal indices of three-dimensional theories related by mirror symmetry

@article{Krattenthaler2011SuperconformalIO,
  title={Superconformal indices of three-dimensional theories related by mirror symmetry},
  author={Christian Krattenthaler and Vyacheslav P. Spiridonov and Grigory S. Vartanov},
  journal={Journal of High Energy Physics},
  year={2011},
  volume={2011},
  pages={1-20}
}
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. 
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