Toward an effective CFT2 from $$ \mathcal{N} $$ = 4 super Yang-Mills and aspects of Hawking radiation

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

Self Cite

“…It clearly suggests the existence of an effective CFT 2 which we have used to microscopically compute the entropy but whose further details we do not know. Some aspects of this effective CFT 2 were studied in [58,59] for the AdS 5 and the AdS 4 black holes, but it required going away from extremality. In the bigger picture described above, understanding how this effective CFT 2 embeds in the boundary CFT d is the dual to finding the UV complete description of the gravitational theory living near the horizon -a worthy challenge.…”

Section: Discussionmentioning

confidence: 99%

Gravitational Cardy limit and AdS black hole entropy

David

Nian

Zayas

2020

Self Cite

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.

“…This would lead us slightly off the supersymmetric sector that is captured by the index. Related to this idea, interesting progress has been reported on near-extremal limits of black hole solutions in[45][46][47].…”

mentioning

confidence: 99%

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.