Asymptotic growth of the 4d $$ \mathcal{N} $$ = 4 index and partially deconfined phases

We explore the gravitational implementation of the field theory Cardy-like limit recently used in the successful microstate countings of AdS black hole entropy in various dimensions. On the field theory side, the Cardy-like limit focuses on a particular scaling of conserved electric charges and angular momenta and we first translate this scaling to the gravitational side by a limiting procedure on the black hole parameters. We note that the scaling naturally accompanies a near-horizon region for which these black hole solutions are greatly simplified. Applying the Kerr/CFT correspondence to the near-horizon region, we precisely reproduce the Bekenstein-Hawking entropy of asymptotically AdS4,5,6,7 BPS black holes. Our results explicitly provide a microscopic and universal low energy description for AdS black holes across various dimensions.

Section: Jhep11(2020)041supporting

confidence: 57%

Gravitational Cardy limit and AdS black hole entropy

David

Nian

Zayas

2020

“…We find that every group homomorphism of a finite abelian group into the torus C/(Zτ + Z) (considered as an abelian group) leads to a solution of the saddle-point equations. The class of solutions that we find includes string-like solutions carrying Z/N Z structure that have been discussed in the literature using the Bethe-ansatz method [12,22,30,31]. The details are presented in section 6.…”

Section: General Saddle-point Configurationsmentioning

confidence: 99%

“…These indices were first calculated in [6,7] in the form of integrals over unitary matrices, and the recent progress involves a detailed study of these integrals. Independent studies in the last couple of years have reached the conclusion that the 1 4 -BPS index in N = 1 theories (or its direct lifts like the 1 16 -BPS in N = 4 SYM) indeed captures the entropy of the dual black hole at large N [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. The basic idea of all the approaches is the same and can be paraphrased as follows: one calculates the index of the BPS states, and shows that it agrees with the "entropy function" of the BPS black hole.…”

Section: Jhep11(2020)150 1 Introduction and Summarymentioning

confidence: 99%

“…The different studies are essentially variants of three approaches, each of which have advantages and disadvantages. One approach is to study the index in a Cardy-like limit [10,13,14,[16][17][18]22]. In this approach the rank N of the gauge group can be finite, but the disadvantage is that the method only applies in the infinite charge limit, or equivalently, to infinitely large black holes.…”

Section: Jhep11(2020)150 1 Introduction and Summarymentioning

confidence: 99%

“…A practical limitation is that it relies on finding solutions to the associated Bethe-ansatz-like equations, which have not been systematically studied so far. It should be said that some families of solutions for specific theories have been found in [12,22,30,31] and, importantly, this includes a solution corresponding to a black hole. Although in this approach the large-N index takes the form of a sum over solutions to the Bethe-ansatz equations, an interpretation of the latter as saddle-points of the integral is not clear (see [12]).…”

Section: Jhep11(2020)150 1 Introduction and Summarymentioning

confidence: 99%

See 2 more Smart Citations

The large-N limit of the 4d $$ \mathcal{N} $$ = 1 superconformal index

Cabo-Bizet

Martelli

Murthy

2020

102

We systematically analyze the large-N limit of the superconformal index of $$ \mathcal{N} $$ N = 1 superconformal theories having a quiver description. The index of these theories is known in terms of unitary matrix integrals, which we calculate using the recently-developed technique of elliptic extension. This technique allows us to easily evaluate the integral as a sum over saddle points of an effective action in the limit where the rank of the gauge group is infinite. For a generic quiver theory under consideration, we find a special family of saddles whose effective action takes a universal form controlled by the anomaly coefficients of the theory. This family includes the known supersymmetric black hole solution in the holographically dual AdS5 theories. We then analyze the index refined by turning on flavor chemical potentials. We show that, for a certain range of chemical potentials, the effective action again takes a universal cubic form that is controlled by the anomaly coefficients of the theory. Finally, we present a large class of solutions to the saddle-point equations which are labelled by group homomorphisms of finite abelian groups of order N into the torus.

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

Lezcano

Hong

Liu

et al. 2021

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.