The topologically twisted index of $$ \mathcal{N} $$ = 4 SU(N) Super-Yang-Mills theory and a black hole Farey tail

We reinterpret the OSV formula for the on-shell action/entropy function of asymptotically flat BPS black holes as a fixed point formula that is formally equivalent to a recent gluing proposal for asymptotically AdS4 black holes. This prompts a conjecture that the complete perturbative answer for the most general gravitational building block of 4d $$ \mathcal{N} $$ N = 2 supergravity at a single fixed point takes the form of a Nekrasov-like partition function with equivariant parameters related to the higher-derivative expansion of the prepotential. In turn this leads to a simple localization-like proposal for a set of supersymmetric partition functions in (UV completed) 4d $$ \mathcal{N} $$ N = 2 supergravity theories. The conjecture is shown to be in agreement with a number of available results for different BPS backgrounds with both Minkowski and AdS asymptotics. In particular, it follows that the OSV formula comes from the unrefined limit of the general expression including only the so-called 𝕎 tower of higher derivatives, while the on-shell action of pure (Euclidean) AdS4 with round S3 boundary comes from the NS limit that includes only the 𝕋 tower. Backgrounds preserving less supersymmetry, such as the under-rotating black holes in flat space, the holographic squashed S3, and the static/rotating twisted and non-twisted Kerr-Newman-like black holes in AdS4 lead to a more general refined version of the corresponding gravitational blocks as dictated by the supersymmetric gluing rules.

Section: Jhep02(2022)079mentioning

confidence: 99%

4d $$ \mathcal{N} $$ = 2 supergravity observables from Nekrasov-like partition functions

Hristov

2022

The SUSY index beyond the Cardy limit

Mamroud

2024

We analyze a set of contributions to the superconformal index of 4d 𝒩 = 4 SU(N) super Yang-Mills using the Bethe Ansatz approach. These contributions dominate at the large N limit, where their leading order in N reproduces various supersymmetric Euclidean black hole saddles in the dual theory, and they also dominate for finite N in high temperature Cardy-like limits. We compute the O(N0) terms, including those exponentially suppressed in the Cardy limit, and show that there are no 1/N corrections beyond them. Under certain assumptions, it implies that the gravitational perturbative series around these black hole saddles is 1-loop exact.

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

Hosseini

Yaakov

Zaffaroni

2022

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 $$ \mathrm{\mathcal{M}}={\mathrm{\mathcal{M}}}_3\times {S}_{\upepsilon}^2 $$ ℳ = ℳ 3 × S ϵ 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 $$ {\mathrm{\mathcal{M}}}_3={\Sigma}_{\mathfrak{g}}\times {S}^1 $$ ℳ 3 = Σ g × S 1 , where $$ {\Sigma}_{\mathfrak{g}} $$ Σ 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×wS4 and AdS7× S4. We also provide the supersymmetric background and explicitly perform localization for the mixed index on $$ {\Sigma}_{\mathfrak{g}}\times {S}^1\times {S}_{\upepsilon}^2 $$ Σ g × S 1 × S ϵ 2 , filling a gap in the literature.