Universal spectrum of 2d conformal field theory in the large c limit

Thomas Hartman, Christoph A. Keller, Bogdan Stoica

Research output: Contribution to journalArticlepeer-review

199 Scopus citations


Abstract: Two-dimensional conformal field theories exhibit a universal free energy in the high temperature limit T → ∞, and a universal spectrum in the Cardy regime, Δ → ∞. We show that a much stronger form of universality holds in theories with a large central charge c and a sparse light spectrum. In these theories, the free energy is universal at all values of the temperature, and the microscopic spectrum matches the Cardy entropy for all Δ ≥c6. The same is true of three-dimensional quantum gravity; therefore our results provide simple necessary and sufficient criteria for 2d CFTs to behave holographically in terms of the leading spectrum and thermodynamics. We also discuss several applications to CFT and gravity, including operator dimension bounds derived from the modular bootstrap, universality in symmetric orbifolds, and the role of non-universal ‘enigma’ saddlepoints in the thermodynamics of 3d gravity.

Original languageEnglish (US)
Article number118
Pages (from-to)1-29
Number of pages29
JournalJournal of High Energy Physics
Issue number9
StatePublished - Sep 2014


  • AdS-CFT Correspondence
  • Field Theories in Lower Dimensions

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


Dive into the research topics of 'Universal spectrum of 2d conformal field theory in the large c limit'. Together they form a unique fingerprint.

Cite this