6d superconformal Cardy formulas

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We explore the supersymmetric partition functions of 6d SCFTs on ℝ4 × T2 with non-vanishing charges for compatible global symmetries. We utilize the elliptic genera for self-dual strings and compute the free energy of 6d SCFTs in the Cardy limit. For a 6d (2,0) theory on N M5-brane, we obtain the free energy proportional to N3. We find that the origin of N3 comes from the condensation of the self-dual strings, whose total number is proportional to $$ \frac{N^3-N}{6} $$ N 3 − N 6 . We further extend our analysis to the general E-string theory and obtain its Cardy free energy.

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confidence: 99%

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confidence: 99%

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confidence: 99%

See 3 more Smart Citations

Cardy limits of 6d superconformal theories

Lee

Nahmgoong

2021

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Universal 3d Cardy block and black hole entropy

Choi

Hwang

2020

We discuss the Cardy limit of 3d supersymmetric partition functions which allow the factorization into the hemisphere indices: the generalized superconformal index, the refined topologically twisted index and the squashed sphere partition function. In the Cardy limit, the hemisphere index can be evaluated by the saddle point approximation where there exists a dominant saddle point contribution, which we call the Cardy block. The Cardy block turns out to be a simple but powerful object as it is a building block of other partition functions in the Cardy limit. The factorization to the Cardy block allows us to find universal relations among the partition functions, which we formulate as index theorems. Furthermore, if we consider a holographic 3d SCFT and its large N limit, those partition functions relate to various entropic quantities of the dual gravity theory in AdS 4 . As a result, our result provides the microscopic derivation of the universal relations among those entropic quantities of the gravity theory. We also discuss explicit examples, which confirm our general index theorems.

How to build a black hole out of instantons

Mouland

2024

An often fruitful route to study quantum gravity is the determination and study of quantum mechanical models — that is, models with finite degrees of freedom — that capture the dynamics of a black hole’s microstates. An example of such a model is the superconformal quantum mechanics of Yang-Mills instantons, which has a proposed gravitational dual description as M-theory on a background of the form X7 × S4. This model arises in the strongly-coupled limit of the BFSS matrix model with additional fundamental hypermultiplets, offering a route towards useful numerical simulation. We construct a six-parameter black hole solution in this theory, which is generically non-supersymmetric and non-extremal, and is shown to arise in an “ultra-spinning” limit of the recently-found six-parameter AdS7 solution. We compute its thermodynamic properties, and show that in the supersymmetric limit the entropy and on-shell action match precisely the expected results as computed from the superconformal index of the quantum mechanics, to leading order in the supergravity regime. The low-lying spectrum thus provides access to the dynamics of near-extremal black holes, whose spectra are expected to receive strong quantum corrections.