Iqbal, AmerVafa, Cumrun2019-09-222014Iqbal, Amer, and Cumrun Vafa. 2014. “BPS Degeneracies and Superconformal Index in Diverse Dimensions.” Physical Review D 90 (10). https://doi.org/10.1103/physrevd.90.105031.1550-23681550-7998http://nrs.harvard.edu/urn-3:HUL.InstRepos:41385101We present a unifying theme relating BPS partition functions and superconformal indices. In the case with complex supersymmetry 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 capture five-dimensional (5d) BPS degeneracies of M theory on Calabi-Yau 3-folds, can be used to compute a 5d supersymmetric index including in the sectors with three-dimensional 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 Superconformal field theory yield the same index.en-USJournal Article2019-09-2210.1103/PhysRevD.90.105031