Rahman's biorthogonal functions and superconformal indices

Abstract

We study biorthogonal functions related to basic hypergeometric integrals with coupled continuous and discrete components. Such integrals appear as superconformal indices for three-dimensional quantum field theories and also in the context of solvable lattice models. We obtain explicit biorthogonal systems given by products of two of Rahman's biorthogonal rational ${}_{10}{W}_9$-functions or their degenerate cases. We also give new bilateral extensions of the Jackson and $q$-Saalschütz summation formulas and new continuous and discrete biorthogonality measures for Rahman's functions.

22 pages

References in corpus (2)

• Generalized Superconformal Index for Three Dimensional Field Theories
• The star-triangle relation, lens partition function, and hypergeometric sum/integrals