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 \( \mathrm{\mathcal{M}}={\mathrm{\mathcal{M}}}_3\times {S}_{\upepsilon}^2 \), 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 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 AdS6 ×w S4 and AdS7 × S4. We also provide the supersymmetric background and explicitly perform localization for the mixed index on \( {\Sigma}_{\mathfrak{g}}\times {S}^1\times {S}_{\upepsilon}^2 \), filling a gap in the literature.
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Hosseini, S.M., Yaakov, I. & Zaffaroni, A. The joy of factorization at large N: five-dimensional indices and AdS black holes. J. High Energ. Phys. 2022, 97 (2022). https://doi.org/10.1007/JHEP02(2022)097
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DOI: https://doi.org/10.1007/JHEP02(2022)097