Holographic microstate counting for AdS4 black holes in massive IIA supergravity

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.

Section: D2-branes Probing a Cy 3-fold Singularity In Massive Iia Strsupporting

confidence: 58%

“…In the small β limit, one can evaluate the integral (2.3) using the saddle point approximation as follows: 19) where N is the gauge group rank. Our effective potential is defined by…”

Section: The Hemisphere Indexmentioning

confidence: 99%

Universal 3d Cardy block and black hole entropy

Choi

Hwang

2020

“…Namely, it has been shown that the topologically twisted index of certain field theory precisely matches the entropy function of the dual magnetically charged asymptotically AdS 4 black holes [7]. Similar microscopic explanations have now been extended to a wide ranges of contexts [8][9][10][11][12] (see the review [13] for a complete list of references).…”

Section: Introductionmentioning

confidence: 86%

Rotating black hole entropy from M5-branes

Benini

Gang

Zayas

2020

We compute the superconformal index of 3d N = 2 superconformal theories obtained from N M5-branes wrapped on a hyperbolic 3-manifold. Exploiting the 3d-3d correspondence we use perturbative invariants of SL(N, C) Chern-Simons theory to determine the superconformal index in the large N limit, including logarithmic in N corrections. The leading order partition function provides a microscopic foundation for the entropy function of the dual rotating asymptotically AdS 4 black holes. We also verify that the supergravity one-loop contribution to the log N term coincides with the field theoretic result. We also propose a 3d-3d formulation for the refined topologically twisted index and provide strong evidence in support of its vanishing which agrees with the fact that the expected dual rotating magnetically charged black hole does not exist, thus providing an interesting link between gravity and a tantalizing mathematical result. 3d T N [M 3 ] theoryWe start with the definition and basic properties of the 3d T N [M 3 ] theory appearing on the LHS of the 3d-3d relation (2.1). We define T N [M 3 ] := the 3d N = 2 superconformal field theory obtained from a twisted compactification of the 6d A N −1 (2,0) theory on M 3 , M 3 = a closed hyperbolic 3-manifold = H 3 /Γ .(2.2)

“…In this case the electromagnetic deformation parameter is a discrete (on/off) deformation, namely, it can be set to c = 0 or 1 without loss of generality [16]. Various AdS 4 [17,18,19], domain-wall [20,19], and black hole [21,22,23,24] solutions have been constructed which necessarily require a non-zero electromagnetic deformation parameter c . Within this massive IIA context, the electromagnetic parameter is identified with the Romans mass parameterF 0 of the ten-dimensional theory [25], and has a holographic interpretation as the Chern-Simons level k of a three-dimensional super-Chern-Simons dual theory [26].…”

Section: Introductionmentioning

confidence: 99%

$$ \mathcal{N} $$ = 2 supersymmetric S-folds

Guarino

Sterckx

Trigiante

2020

176

Multi-parametric families of AdS 4 vacua with various amounts of supersymmetry and residual gauge symmetry are found in the [SO(1, 1) × SO(6)] ⋉ R 12 maximal supergravity that arises from the reduction of type IIB supergravity on R × S 5 . These provide natural candidates to holographically describe new strongly coupled three-dimensional CFT's which are localised on interfaces of N = 4 super-Yang-Mills theory. One such AdS 4 vacua features a symmetry enhancement to SU(2) × U(1) while preserving N = 2 supersymmetry. Fetching techniques from the E 7(7) exceptional field theory, its uplift to a class of N = 2 S-folds of type IIB supergravity of the form AdS 4 × S 1 × S 5 involving S-duality twists of hyperbolic type along S 1 is presented.