Gravitational Cardy limit and AdS black hole entropy

Self Cite

We systematically study various sub-leading structures in the superconformal index of $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory with SU(N) gauge group. We concentrate in the superconformal index description as a matrix model of elliptic gamma functions and in the Bethe-Ansatz presentation. Our saddle-point approximation goes beyond the Cardy-like limit and we uncover various saddles governed by a matrix model corresponding to SU(N) Chern-Simons theory. The dominant saddle, however, leads to perfect agreement with the Bethe-Ansatz approach. We also determine the logarithmic correction to the superconformal index to be log N, finding precise agreement between the saddle-point and Bethe-Ansatz approaches in their respective approximations. We generalize the two approaches to cover a large class of 4d $$ \mathcal{N} $$ N = 1 superconformal theories. We find that also in this case both approximations agree all the way down to a universal contribution of the form log N. The universality of this last result constitutes a robust signature of this ultraviolet description of asymptotically AdS5 black holes and could be tested by low-energy IIB supergravity.

Section: Discussionmentioning

confidence: 96%

Sub-leading structures in superconformal indices: subdominant saddles and logarithmic contributions

Lezcano

Hong

Liu

et al. 2021

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“…Consequently, it provided a new microscopic formalism of Hawking radiation, similar to the D1-D5 CFT interpretation for asymptotically flat black holes studied by Callan and Maldacena [26]. In this work, we extend the analyses of [22] from the BPS case to the near-extremal case. However, unlike [22], we do not assume the Cardy limit.…”

Section: Introductionmentioning

confidence: 75%

“…More precisely, for BPS black holes, their entropies can be computed in various ways, including (i) the original Bekenstein-Hawking formula on the gravity side, (ii) the near-horizon Kerr/CFT correspondence and (iii) the microstate counting from the boundary CFT via AdS/CFT correspondence. In addition, the useful limit called the gravitational Cardy limit can simplify the geometry near the horizon, by producing an AdS 3 subgeometry, which has been explicitly verified for AdS 4,5,6,7 BPS black holes in [22].…”

Section: Introductionmentioning

confidence: 93%

“…This is made explicit in this paper by imposing the near-extremal condition (2.20) with the parameter a fixed by the supersymmetric condition (2.7). Moreover, we perform a near-horizon scaling to the asymptotically AdS 4 black hole metric (2.4), which was first introduced by Bardeen and Horowitz in [25] and extensively studied [22] for the BPS AdS 4 black holes…”

Section: Ads 4 Black Hole Solution In the Near-horizon Limitmentioning

confidence: 99%

“…In this work, we extend the analyses of [22] from the BPS case to the near-extremal case. However, unlike [22], we do not assume the Cardy limit.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Universal entropy and hawking radiation of near-extremal AdS4 black holes

David

Nian

2021

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We compute the Bekenstein-Hawking entropy of near-extremal asymptotically AdS4 electrically charged rotating black holes using three different methods: (i) from the gravity solution, (ii) from the near-horizon Kerr/CFT correspondence and (iii) from the boundary conformal field theory. The results from these three different approaches match exactly, giving us a unique and universal expression for the entropy and the microstate counting of near-extremal AdS black holes via the AdS/CFT correspondence. In the second method, we extend the Kerr/CFT correspondence to the near-extremal case to compute the left and right central charges. We also use hidden conformal symmetry of the near-horizon geometry to compute the Frolov-Thorne temperatures. From the results of the near-extremal AdS4 black hole entropy, we provide a microscopic foundation for Hawking radiation.

Cardy expansion of 3d superconformal indices and corrections to the dual black hole entropy

Lezcano

Jerdee

Zayas

2023

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We consider the superconformal index of three-dimensional $$ \mathcal{N} $$ N = 2 supersymmetric field theories computed via localization on S1 × S2. We systematically develop an expansion where the ratio of the radius of S1 to the radius of S2 is taken very small — a Cardy-like expansion. We emphasize the sub-leading structures in this Cardy-like expansion as well as their interplay with the large-N limit for theories with gauge group of the form product of U(N) factors. We demonstrate that taking the large-N limit first leads to an expression for the effective action yielding the index that only includes terms proportional to 1/β and powers of βi=0,1,2 where β is the ratio of radii. As we depart from the β → 0 limit for finite N, we find indications of non-perturbative contributions of the form e−1/β. We present an explicit evaluation of the superconformal index for the ABJM theory in the large-N limit that is exact in β up to non-perturbative corrections. For the ABJM theory we explore the implications of the Cardy-like expansion for corrections to the entropy of the rotating, electricallly charged, asymptotically AdS4 dual black hole. Interestingly, we find a closed form for the entropy that includes all perturbative corrections in β and takes the form of the leading order expression but with shifted charges.