Residues, modularity, and the Cardy limit of the 4d $\mathcal{N}=4$ superconformal index

Goldstein, Kevin; Jejjala, Vishnu; Lei, Yang; van Leuven, Sam; Li, Wei

doi:10.48550/arxiv.2011.06605

Cited by 9 publications

(49 citation statements)

References 52 publications

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“…We interpret the latter cases as unstable, perhaps to condensation of these D3-branes that would take us to some other background. Thus, we consider a gravitational background to be stable only if every D3brane satisfies 23 Im(S D3 ) > 0 ,…”

Section: The Brane Actionmentioning

confidence: 99%

A gravity interpretation for the Bethe Ansatz expansion of the $\mathcal{N}=4$ SYM index

Aharony,

Benini,

Mamroud

et al. 2021

Preprint

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The superconformal index of the N = 4 SU(N) supersymmetric Yang-Mills theory counts the 1/16-BPS states in this theory, and has been used via the AdS/CFT correspondence to count black hole microstates of 1/16-BPS black holes. On one hand, this index may be related to the Euclidean partition function of the theory on S 3 × S 1 with complex chemical potentials, which maps by the AdS/CFT correspondence to a sum over Euclidean gravity solutions. On the other hand, the index may be expressed as a sum over solutions to Bethe Ansatz Equations (BAEs). We show that the known solutions to the BAEs that have a good large N limit, for the case of equal chemical potentials for the two angular momenta, have a one-to-one mapping to (complex) Euclidean black hole solutions on the gravity side. This mapping captures both the leading contribution from the classical gravity action (of order N 2 ), as well as non-perturbative corrections in 1/N, which on the gravity side are related to wrapped D3-branes. Some of the BA solutions map to orbifolds of the standard Euclidean black hole solutions (that obey exactly the same boundary conditions as the other solutions). A priori there are many more gravitational solutions than Bethe Ansatz solutions, but we show that by considering the non-perturbative effects, the extra solutions are ruled out, leading to a precise match between the solutions on both sides.

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Section: The Brane Actionmentioning

confidence: 99%

A gravity interpretation for the Bethe Ansatz expansion of the $\mathcal{N}=4$ SYM index

Aharony,

Benini,

Mamroud

et al. 2021

Preprint

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show abstract

“…The group element then relates the complex structures of two solid T 3 torus. Such factorization structure can also be observed in N = 4 SYM [40]. It is interesting to know whether such factorization structure can survive at the one-loop level with the Spin Matrix theory coupling turned on and also what is the corresponding effect on the 2d elliptic genera.…”

Section: Discussionmentioning

confidence: 90%

Symmetry structure of the interactions in near-BPS corners of $ \mathcal{N} = 4$ super-Yang-Mills

Baiguera,

Harmark,

Lei

et al. 2020

Preprint

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We consider limits of N = 4 super-Yang-Mills (SYM) theory that approach BPS bounds. These limits result in non-relativistic near-BPS theories that describe the effective dynamics near the BPS bounds and upon quantization are known as Spin Matrix theories. The near-BPS theories can be obtained by reducing N = 4 SYM on a three-sphere and integrating out the fields that become non-dynamical in the limits. We perform the sphere reduction for the near-BPS limit with SU(1, 2|2) symmetry, which has several new features compared to the previously considered cases with SU(1, 1) symmetry, including a dynamical gauge field. We discover a new structure in the classical limit of the interaction term. We show that the interaction term is built from certain blocks that comprise an irreducible representation of the SU(1, 2|2) algebra. Moreover, the full interaction term can be interpreted as a norm in the linear space of this representation, explaining its features including the positive definiteness. This means one can think of the interaction term as a distance squared from saturating the BPS bound. The SU(1, 1|1) near-BPS theory, and its subcases, is seen to inherit these features. These observations point to a way to solve the strong coupling dynamics of these near-BPS theories.

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“…Let us now consider the simple algebra g of a simple Lie group G, and focus on the (simultaneous) poles from the ϑ 4 's in the denominator given by the equations [16,34] e 2πiαi(a) = bq…”

Section: And Use ∆ +mentioning

confidence: 99%

“…It is straightforward to compute the residue of the full integrand at the poles [16,34]. We first present the raw result before further massage (we have dropped the overall sign and 1/|W | to avoid clutter, and written the theta functions in terms of (z; q)), which reads Res = q |∆|+r 8 (q; q) 3r [(q; q)(bq…”

Section: And Use ∆ +mentioning

confidence: 99%

Defects, modular differential equations, and free field realization of N = 4 VOAs

Pan,

Wang,

Zheng

2021

Preprint

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For all 4d N = 4 SYM theories with simple gauge groups G, we show that the residues of the integrands in the N = 4 Schur indices, which are related to Gukov-Witten type surface defects in the theories, equal the vacuum characters of rank G copies of bcβγ systems that provide the free field realization of associated N = 4 VOAs in [1]. This result predicts that these residues, as module characters, are additional solutions to the flavored modular differential equations satisfied by the original Schur index. The prediction is verified in the G = SU (2) case, where an additional logarithmic solution is constructed.

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Residues, modularity, and the Cardy limit of the 4d $\mathcal{N}=4$ superconformal index

Cited by 9 publications

References 52 publications

A gravity interpretation for the Bethe Ansatz expansion of the $\mathcal{N}=4$ SYM index

A gravity interpretation for the Bethe Ansatz expansion of the $\mathcal{N}=4$ SYM index

Symmetry structure of the interactions in near-BPS corners of $ \mathcal{N} = 4$ super-Yang-Mills

Defects, modular differential equations, and free field realization of N = 4 VOAs

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