Lectures on the Superconformal Index

Gadde, Abhijit

doi:10.48550/arxiv.2006.13630

Cited by 9 publications

(15 citation statements)

References 40 publications

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“…Before turning to the computation, we will describe the index in some detail and in the process set up notation. See [40] for a recent review.…”

Section: Computation Of the N = 4 Indexmentioning

confidence: 99%

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

Goldstein,

Jejjala,

Lei

et al. 2020

Preprint

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We compute the superconformal index of the N = 4 SU (N ) Yang-Mills theory through a residue calculation. The method is similar in spirit to the Bethe Ansatz formalism, except that all poles are explicitly known, and we do not require specialization of any of the chemical potentials. Our expression for the index allows us to revisit the Cardy limit using modular properties of four-dimensional supersymmetric partition functions. We find that all residues contribute at leading order in the Cardy limit. In a specific region of flavour chemical potential space, close to the two unrefined points, in fact all residues contribute universally. These universal residues precisely agree with the entropy functions of the asymptotically AdS 5 black hole and its "twin saddle" respectively. Finally, we discuss how our formula is suited to study the implications of four-dimensional modularity for the index beyond the Cardy limit.

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“…Before turning to the computation, we will describe the index in some detail and in the process set up notation. See [40] for a recent review.…”

Section: Computation Of the N = 4 Indexmentioning

confidence: 99%

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

Goldstein,

Jejjala,

Lei

et al. 2020

Preprint

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“…A related question would be then under which conditions we can find say N = 1 Lagrangians with manifest global symmetry for such models. 60 General types of punctures: 5d UV dualities A useful knob in constructing 4d theories corresponding to a surface is through gluing theories corresponding to smaller surfaces with the gluing done along a puncture. A given 6d SCFT might have a variety of types of maximal punctures along which we can glue.…”

Section: Gauging Emergent Symmetriesmentioning

confidence: 99%

Aspects of 4d supersymmetric dynamics and geometry

Razamat¹,

Sabag²,

Sela³

et al. 2022

Preprint

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In this set of five lectures we present a basic toolbox to discuss the dynamics of four dimensional supersymmetric quantum field theories. In particular we overview the program of geometrically engineering the four dimensional supersymmetric models as compactifications of six dimensional SCFTs. We discuss how strong coupling phenomena in four dimensions, such as duality and emergence of symmetry, can be naturally imbedded in the geometric constructions. The lectures mostly review results which previously appeared in the literature but also contain some unpublished derivations.

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“…The superconformal index of the N = 4 SU (N ) super-Yang-Mills theory is defined as the weighted trace over the Hilbert space H of the theory quantized on S 3 . A recent review is [52]. Explicitly, the index is defined as [12]:…”

Section: Plan Of Papermentioning

confidence: 99%

$SL(3,\mathbb{Z})$ Modularity and New Cardy Limits of the $\mathcal{N}=4$ Superconformal Index

Jejjala,

Lei,

van Leuven

et al. 2021

Preprint

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The entropy of 1/16-th BPS AdS 5 black holes can be microscopically accounted for by the superconformal index of the 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 N = 4 superconformal index. From these limits, we obtain entropy formulae that have a similar form as that of the original AdS 5 black hole, up to an overall rescaling of the entropy and a shift in the charges. 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 story to four dimensions.

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Lectures on the Superconformal Index

Cited by 9 publications

References 40 publications

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

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

Aspects of 4d supersymmetric dynamics and geometry

$SL(3,\mathbb{Z})$ Modularity and New Cardy Limits of the $\mathcal{N}=4$ Superconformal Index

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