BPS Degeneracies and Superconformal Index in Diverse Dimensions

TL;DR

This paper unifies the understanding of BPS partition functions and superconformal indices across various dimensions, revealing how BPS degeneracies relate to superconformal indices in different supersymmetric theories and geometries.

Contribution

It introduces a unified framework connecting BPS partition functions with superconformal indices in diverse dimensions and supersymmetry contexts, including complex and real central charge cases.

Findings

BPS partition functions can compute specialized superconformal indices in certain SUSY theories.

In some cases, BPS degeneracies capture the full superconformal index.

Refined topological strings relate to 5d superconformal indices, including sectors with 3d defects.

Abstract

We present a unifying theme relating BPS partition functions and superconformal indices. In the case with complex SUSY central charges (as in N=2 in d=4 and N=(2,2) in d=2) the known results can be reinterpreted as the statement that the BPS partition functions can be used to compute a specialization of the superconformal indices. We argue that in the case with real central charge in the supersymmetry algebra, as in N=1 in d=5 (or the N=2 in d=3), the BPS degeneracy captures the full superconformal index. Furthermore, we argue that refined topological strings, which captures 5d BPS degeneracies of M-theory on CY 3-folds, can be used to compute 5d supersymmetric index including in the sectors with 3d defects for a large class of 5d superconformal theories. Moreover, we provide evidence that distinct Calabi-Yau singularities which are expected to lead to the same SCFT yield the same index.