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SL(3, ℤ) Modularity and New Cardy limits of the N $$ \mathcal{N} $$ = 4 superconformal index
- Source :
- Journal of High Energy Physics, Vol 2021, Iss 11, Pp 1-77 (2021), Journal of High Energy Physics
- Publication Year :
- 2021
- Publisher :
- SpringerOpen, 2021.
-
Abstract
- 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.
- Subjects :
- Physics
Nuclear and High Energy Physics
Pure mathematics
Generalization
Function (mathematics)
QC770-798
AdS-CFT Correspondence
Supersymmetric Gauge Theory
Black hole
Entropy (classical thermodynamics)
Integer
Nuclear and particle physics. Atomic energy. Radioactivity
Black Holes in String Theory
Farey sequence
Field theory (psychology)
Limit (mathematics)
Subjects
Details
- Language :
- English
- ISSN :
- 10298479
- Volume :
- 2021
- Issue :
- 11
- Database :
- OpenAIRE
- Journal :
- Journal of High Energy Physics
- Accession number :
- edsair.doi.dedup.....18ca2adc2673586f941584ef22af0f50