EFT and the SUSY index on the 2nd sheet

Komargodski, Zohar

doi:10.21468/scipostphys.11.1.004

Cited by 47 publications

(72 citation statements)

References 82 publications

(192 reference statements)

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“…At leading order the resulting expression for the superconformal index does indeed match the entropy function of AdS 5 × S 5 black holes [22], both in the large-N limit [21,[23][24][25][26][27] and in the limit of large conserved charges (i.e. the Cardy limit) [20,24,[28][29][30][31][32][33][34][35]. The entropy function is the Legendre transform of the black hole entropy; it can also be written as the complexified on-shell action of the Euclidean black hole geometry [36,37].…”

Section: Introductionmentioning

confidence: 77%

“…The entropy function is the Legendre transform of the black hole entropy; it can also be written as the complexified on-shell action of the Euclidean black hole geometry [36,37]. These results for the computation of the superconformal index have also been extended to the case of more general N = 1 gauge theories [25,[38][39][40] [30,33,34,[41][42][43][44].…”

Section: Introductionmentioning

confidence: 92%

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The large-$N$ limit of 4d superconformal indices for general BPS charges

Colombo¹

2021

Preprint

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We study the superconformal index of N = 1 quiver theories at large -N for general values of electric charges and angular momenta, using both the Bethe Ansatz formulation and the more recent elliptic extension method. We are particularly interested in the case of unequal angular momenta, J 1 = J 2 , which has only been partially considered in the literature. We revisit the previous computation with the Bethe Ansatz formulation with generic angular momenta and extend it to encompass a large class of competing exponential terms. In the process, we also provide a simplified derivation of the original result. We consider the newly-developed elliptic extension method as well; we apply it to the J 1 = J 2 case, finding a good match with the Bethe Ansatz results. We also investigate the relation between the two different approaches, finding in particular that for every saddle of the elliptic action there are corresponding terms in the Bethe Ansatz formula that match it at large -N. Contents 1 Introduction 1 2 The superconformal index of quiver theories 4 3 Large -N saddle points and the effective action 8 3.1 Contour deformation 3.2 Continuum limit 3.3 String-like saddles 3.4 General saddles 4 The large -N limit with the Bethe Ansatz formula 22 4.1 The Bethe Ansatz formula 4.2 BAE solutions and saddle points of the elliptic action 4.3 Evaluation of the index 4.4 Relation with previous work and competing exponential terms 5 Summary and discussion 35 A The elliptic gamma and related functions 36 B Subleading terms in the Bethe Ansatz formula 40Recently, the case of Kerr-Newman BPS black holes in AdS 5 has attracted a lot of interest. There are known BPS black hole solutions for type IIB supergravity in AdS 5 × S 5 which

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Section: Introductionmentioning

confidence: 77%

Section: Introductionmentioning

confidence: 92%

The large-$N$ limit of 4d superconformal indices for general BPS charges

Colombo¹

2021

Preprint

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“…Note added. The paper [84], which appeared on the arXiv the same day as the first version of this paper, has some overlap with our section 3. The paper [87], which appeared on the arXiv soon after, has some overlap with our section 2.…”

Section: Jhep10(2021)207mentioning

confidence: 94%

“…The recent work[84] presents such a derivation, although using a background different from ours. The precise relation between the two backgrounds is not clear to us at the moment.…”

mentioning

confidence: 99%

The 4d superconformal index near roots of unity and 3d Chern-Simons theory

Ardehali

Murthy

2021

J. High Energ. Phys.

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We consider the S3×S1 superconformal index ℐ(τ) of 4d $$ \mathcal{N} $$ N = 1 gauge theories. The Hamiltonian index is defined in a standard manner as the Witten index with a chemical potential τ coupled to a combination of angular momenta on S3 and the U(1) R-charge. We develop the all-order asymptotic expansion of the index as q = e2πiτ approaches a root of unity, i.e. as $$ \overset{\sim }{\tau } $$ τ ~ ≡ mτ+n → 0, with m, n relatively prime integers. The asymptotic expansion of log ℐ(τ) has terms of the form $$ \overset{\sim }{\tau } $$ τ ~ k, k = −2, −1, 0, 1. We determine the coefficients of the k = −2, −1, 1 terms from the gauge theory data, and provide evidence that the k = 0 term is determined by the Chern-Simons partition function on S3/ℤm. We explain these findings from the point of view of the 3d theory obtained by reducing the 4d gauge theory on the S1. The supersymmetric functional integral of the 3d theory takes the form of a matrix integral over the dynamical 3d fields, with an effective action given by supersymmetrized Chern-Simons couplings of background and dynamical gauge fields. The singular terms in the $$ \overset{\sim }{\tau } $$ τ ~ → 0 expansion (dictating the growth of the 4d index) are governed by the background Chern-Simons couplings. The constant term has a background piece as well as a piece given by the localized functional integral over the dynamical 3d gauge multiplet. The linear term arises from the supersymmetric Casimir energy factor needed to go between the functional integral and the Hamiltonian index.

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“…Further developments on the N = 4 index and its relation to AdS 5 black holes include [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. These methods have also been extended to the analysis of superconformal field theories with N = 1 supersymmetry [32][33][34][35][36][37][38][39][40]. Connections with AdS 3 /CFT 2 , specifically the twodimensional Cardy formula and near horizon limits of the AdS 5 black holes, were explored in [41][42][43].…”

Section: Jhep11(2021)047 1 Introduction and Summarymentioning

confidence: 99%

SL(3, ℤ) Modularity and New Cardy limits of the $$ \mathcal{N} $$ = 4 superconformal index

Jejjala

Lei

Leuven

et al. 2021

J. High Energ. Phys.

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The entropy of 1/16-th BPS AdS5 black holes can be microscopically accounted for by the superconformal index of the $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory. One way to compute this is through a Cardy-like limit of a formula for the index obtained in [1] using the “S-transformation” of the elliptic Γ function. In this paper, we derive more general SL(3, ℤ) modular properties of the elliptic Γ function. We then use these properties to obtain a three integer parameter family of generalized Cardy-like limits of the $$ \mathcal{N} $$ N = 4 superconformal index. From these limits, we obtain entropy formulae that have a similar form as that of the original AdS5 black hole, up to an overall rescaling of the entropy. We interpret this both on the field theory and the gravitational side. Finally, we comment on how our work suggests a generalization of the Farey tail to four dimensions.

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EFT and the SUSY index on the 2nd sheet

Cited by 47 publications

References 82 publications

The large-$N$ limit of 4d superconformal indices for general BPS charges

The large-$N$ limit of 4d superconformal indices for general BPS charges

The 4d superconformal index near roots of unity and 3d Chern-Simons theory

SL(3, ℤ) Modularity and New Cardy limits of the $$ \mathcal{N} $$ = 4 superconformal index

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