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

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 M = M-3 x S-epsilon(2), where epsilon is an equivariant parameter for rotation. We show that, when M-3 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 M-3 = Sigma(g) x S-1, where Sigma(g) is a Riemann surface of genus g, 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 AdS(6) x S-w(4) and AdS(7) x S-4. We also provide the supersymmetric background and explicitly perform localization for the mixed index on Sigma(g) x S-1 x S-epsilon(2), filling a gap in the literature.

Automated summary

In this paper, we discuss the large N factorization properties of five-dimensional supersymmetric partition functions for CFT with holographic dual. We provide examples to demonstrate the calculation method of partition functions for various observables.