Elliptic hypergeometric integrals and 't Hooft anomaly matching   conditions
  Elliptic hypergeometric integrals describe superconformal indices of 4d supersymmetric field theories. We show that all 't Hooft anomaly matching conditions for Seiberg dual theories can be derived from $SL(3,\mathbb{Z})$-modular transformation properties of the kernels of dual indices. 
V. P. Spiridonov, G. S. Vartanov
hep-th