Supersymmetric indices factorize

A bstract The extent to which quantum mechanical features of black holes can be understood from the Euclidean gravity path integral has recently received significant attention. In this paper, we examine question for calculation supersymmetric index. For concreteness, focus on case charged in asymptotically flat four-dimensional $$ \mathcal{N} N = 2 ungauged supergravity. We show that with boundary conditions an infinite family Kerr-Newman classical saddles different angular velocities. argue fermionic zero-mode fluctuations are present around each these solutions making their contribution vanish, except a single saddle is BPS and gives expected value then turn non-perturbative corrections involving spacetime wormholes zero mode all geometries, vanish once again. This mechanism works both single- multi-boundary integrals. particular, only disconnected geometries without contribute gravitational computes index, factorization puzzle plagues hole partition function resolved Finally, classify other single-centered yield contributions index boundary.