The asymptotic growth of states of the 4d N= 1 superconformal index

Alejandro Cabo-Bizet, Davide Cassani*, Dario Martelli, Sameer Murthy

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

69 Citations (Scopus)


We show that the superconformal index of N= 1 superconformal field theories in four dimensions has an asymptotic growth of states which is exponential in the charges. Our analysis holds in a Cardy-like limit of large charges, for which the index is dominated by small values of chemical potentials. In this limit we find the saddle points of the integral that defines the superconformal index using two different methods. One method, valid for finite N, is to first take the Cardy-like limit and then find the saddle points. The other method is to analyze the saddle points at large N and then take the Cardy-like limit. The result of both analyses is that the asymptotic growth of states of the superconformal index exactly agrees with the Bekenstein-Hawking entropy of supersymmetric black holes in the dual AdS5 theory.

Original languageEnglish
Article number120
JournalJournal of High Energy Physics
Issue number8
Early online date22 Aug 2019
Publication statusE-pub ahead of print - 22 Aug 2019


  • AdS-CFT Correspondence
  • Black Holes in String Theory
  • Conformal Field Theory
  • Supersymmetric Gauge Theory


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