The most irrational rational theories

  • Nathan BenjaminEmail author
  • Ethan Dyer
  • A. Liam Fitzpatrick
  • Yuan Xin
Open Access
Regular Article - Theoretical Physics


We propose a two-parameter family of modular invariant partition functions of two-dimensional conformal field theories (CFTs) holographically dual to pure three-dimensional gravity in anti de Sitter space. Our two parameters control the central charge, and the representation of SL(2, ℤ). At large central charge, the partition function has a gap to the first nontrivial primary state of \( \frac{c}{24} \). As the SL(2, ℤ) representation dimension gets large, the partition function exhibits some of the qualitative features of an irrational CFT. This, for instance, is captured in the behavior of the spectral form factor. As part of these analyses, we find similar behavior in the minimal model spectral form factor as c approaches 1.


AdS-CFT Correspondence Conformal and W Symmetry Conformal Field Theory Field Theories in Lower Dimensions 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Stanford Institute for Theoretical PhysicsStanfordU.S.A.
  2. 2.Physics DepartmentBoston UniversityBostonU.S.A.
  3. 3.Princeton Center for Theoretical SciencePrinceton UniversityPrincetonU.S.A.
  4. 4.Department of Physics and AstronomyJohns Hopkins UniversityBaltimoreU.S.A.
  5. 5.GoogleMountain ViewU.S.A.

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