The joy of factorization at large N: five-dimensional indices and AdS black holes

Abstract

We discuss the large N factorization properties of five-dimensional supersymmetric partition functions for CFT with a holographic dual. We consider partition functions on manifolds of the form mathrm{mathcal{M}}={mathrm{mathcal{M}}}_3times {S}_{upepsilon}^2 , where ϵ is an equivariant parameter for rotation. We show that, when ℳ3 is a squashed three-sphere, the large N partition functions can be obtained by gluing elementary blocks associated with simple physical quantities. The same is true for various observables of the theories on {mathrm{mathcal{M}}}_3={Sigma}_{mathfrak{g}}times {S}^1 , where {Sigma}_{mathfrak{g}} is a Riemann surface of genus \U0001d524, and, with a natural assumption on the form of the saddle point, also for the partition function, corresponding to either the topologically twisted index or a mixed one. This generalizes results in three and four dimensions and correctly reproduces the entropy of known black objects in AdS6×wS4 and AdS7× S4. We also provide the supersymmetric background and explicitly perform localization for the mixed index on {Sigma}_{mathfrak{g}}times {S}^1times {S}_{upepsilon}^2 , filling a gap in the literature.