Bethe Ansatz for the superconformal index with unequal angular momenta

Ofer Aharony (Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 7610001, Israel; School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540, USA) ; Ohad Mamroud (Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 7610001, Israel; SISSA, Via Bonomea 265, 34136 Trieste, Italy; INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy) ; Shimon Nowik (Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 7610001, Israel) ; Meir Weissman (Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 7610001, Israel)

A few years ago it was shown that the superconformal index of the N=4 supersymmetric SU(N) Yang-Mills theory in the large N limit matches with the entropy of 1/16-supersymmetric black holes in type IIB string theory on AdS5×S5. In some cases, an even more detailed match between the two sides is possible. When the two angular momentum chemical potentials in the index are equal, the superconformal index can be written as a discrete sum of Bethe ansatz solutions, and it was shown that specific terms in this sum are in a one-to-one correspondence to stable black hole solutions, and that the matching can be extended to nonperturbative contributions from wrapped D3-branes. A Bethe ansatz approach to computing the superconformal index exists also when the ratio of the angular momentum chemical potentials is any rational number, but in those cases it involves a sum over a very large number of terms (growing exponentially with N). Benini et al. showed that a specific one of these terms matches with the black hole, but the role of the other terms is not clear. In this paper we analyze some of the additional contributions to the index in the Bethe ansatz approach, and we find that their matching to the gravity side is much more complicated than in the case of equal chemical potentials. In particular, we find some contributions that are larger than the one that was found to match the black holes, in which case they must cancel with other large contributions. We give some evidence that cancellations of this type are possible, but we leave a full understanding of how they work to the future.

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      "value": "A few years ago it was shown that the superconformal index of the <math><mi>N</mi><mo>=</mo><mn>4</mn></math> supersymmetric <math><mi>S</mi><mi>U</mi><mo>(</mo><mi>N</mi><mo>)</mo></math> Yang-Mills theory in the large <math><mi>N</mi></math> limit matches with the entropy of <math><mn>1</mn><mo>/</mo><mn>16</mn></math>-supersymmetric black holes in type IIB string theory on <math><msub><mi>AdS</mi><mn>5</mn></msub><mo>\u00d7</mo><msup><mi>S</mi><mn>5</mn></msup></math>. In some cases, an even more detailed match between the two sides is possible. When the two angular momentum chemical potentials in the index are equal, the superconformal index can be written as a discrete sum of Bethe ansatz solutions, and it was shown that specific terms in this sum are in a one-to-one correspondence to stable black hole solutions, and that the matching can be extended to nonperturbative contributions from wrapped D3-branes. A Bethe ansatz approach to computing the superconformal index exists also when the ratio of the angular momentum chemical potentials is any rational number, but in those cases it involves a sum over a very large number of terms (growing exponentially with <math><mi>N</mi></math>). Benini et al. showed that a specific one of these terms matches with the black hole, but the role of the other terms is not clear. In this paper we analyze some of the additional contributions to the index in the Bethe ansatz approach, and we find that their matching to the gravity side is much more complicated than in the case of equal chemical potentials. In particular, we find some contributions that are larger than the one that was found to match the black holes, in which case they must cancel with other large contributions. We give some evidence that cancellations of this type are possible, but we leave a full understanding of how they work to the future."
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Published on:
22 April 2024
Publisher:
APS
Published in:
Physical Review D , Volume 109 (2024)
Issue 8
DOI:
https://doi.org/10.1103/PhysRevD.109.085015
arXiv:
2402.03977
Copyrights:
Published by the American Physical Society
Licence:
CC-BY-4.0

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