The large-N limit 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

33 Citations (Scopus)


We systematically analyze the large-N limit of the superconformal index of N = 1 superconformal theories having a quiver description. The index of these theories is known in terms of unitary matrix integrals, which we calculate using the recently-developed technique of elliptic extension. This technique allows us to easily evaluate the integral as a sum over saddle points of an effective action in the limit where the rank of the gauge group is infinite. For a generic quiver theory under consideration, we find a special family of saddles whose effective action takes a universal form controlled by the anomaly coefficients of the theory. This family includes the known supersymmetric black hole solution in the holographically dual AdS5 theories. We then analyze the index refined by turning on flavor chemical potentials. We show that, for a certain range of chemical potentials, the effective action again takes a universal cubic form that is controlled by the anomaly coefficients of the theory. Finally, we present a large class of solutions to the saddle-point equations which are labelled by group homomorphisms of finite abelian groups of order N into the torus.

Original languageEnglish
Article number150
JournalJournal of High Energy Physics
Issue number11
Publication statusPublished - Nov 2020


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


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