Supersymmetric localization of refined chiral multiplets on topologically twisted H2 × S1

We derive the partition function of an N=2 chiral multiplet on topologically twisted H2×S1. The chiral multiplet is coupled to a background vector multiplet encoding a real mass deformation. We consider an H2×S1 metric containing two parameters: one is the S1 radius, while the other gives a fugacity q for the angular momentum on H2. The computation is carried out by means of supersymmetric localization, which provides a finite answer written in terms of q-Pochammer symbols and multiple Zeta functions. Especially, the partition function of normalizable fields reproduces three-dimensional holomorphic blocks.