Title: [NTU-NCTS String Seminar] Modular factorization of superconformal indices
Speaker: Dr. Sam van Leuven (Wits University)
Time: Nov. 18, 2022 (Fri.) 14:30-15:30
Venue: Rm. 815, Dept. of Physics, NTU

Abstract:
Recent work has revisited the study of supersymmetric black holes in AdS(d>3) spaces from the perspective of the dual CFT. Asymptotic limits of the superconformal index have been shown to reproduce the Bekenstein-Hawking entropy exactly. In AdS(5), an unconventional modular property of the elliptic Gamma function plays a crucial role. This property has made an earlier appearance in the context of holomorphic block factorization of superconformal indices of general four-dimensional N=1 gauge theories. We provide a precise physical interpretation of the modular property as resulting from the combined action of an SL(3,Z) and SL(2,Z)xZ2 transformation. The former corresponds to a gluing transformation and the latter to an overall large diffeomorphism, both associated with a Heegaard splitting of the underlying geometry. The extension to more general transformations leads us to conjecture the ``modular factorization'' of superconformal lens indices: a given index can be factorized in terms of a family of holomorphic blocks parametrized by modular (congruence sub)groups. We find precise agreement between this proposal and general modular properties of the elliptic Gamma function. If time permits, I will discuss how this result allows a systematic proof of the fact that a normalized part of superconformal lens indices defines a non-trivial first cohomology class associated with SL(3,Z).