2023/07/21 by Iannotti, Daniele, Pittelli, Antonio
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2307.11634
We introduce the topologically twisted index for four-dimensional \mathcal N=1 gauge theories quantized on \rm AdS2 × S1. We compute the index by applying supersymmetric localization to partition functions of vector and chiral multiplets on \rm AdS2 × T2, with and without a boundary: in both instances we classify normalizability and boundary conditions for gauge, matter and ghost fields. The index is twisted as the dynamical fields are coupled to a R-symmetry background 1-form with non-trivial exterior derivative and proportional to the spin connection. After regularization the index is written in terms of elliptic gamma functions, reminiscent of four-dimensional holomorphic blocks, and crucially depends on the R-charge.