A Refined N=2 Chiral Multiplet on Twisted AdS2 x S¹

Authors: Antonio Pittelli

Preprint number: UUITP-63/18

N=2 chiral multiplet on twisted AdS₂×S¹. The chiral multiplet is coupled to a background vector multiplet encoding a real mass deformation. We consider an AdS₂×S¹ metric containing two parameters: one is the S¹ radius, while the other gives a fugacity q for the angular momentum on AdS₂. The computation is carried out by means of supersymmetric localisation, which provides a finite answer written in terms of q-Pochammer symbols and multiple Zeta functions. Especially, the partition function Z_chi reproduces three-dimensional holomorphic blocks if we require that all the fields are strictly normalisable. Finally, we observe that Z_chi loses its dependence on the S¹ radius once the background vector multiplet is turned off, becoming a pure function of the fugacity q.