The most irrational rational theories

• Published in: The journal of high energy physics Vol. 2019; no. 4; pp. 1 - 35
• Main Authors: Benjamin, Nathan, Dyer, Ethan, Fitzpatrick, A. Liam, Xin, Yuan
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2019; Springer Nature B.V; Springer Berlin; SpringerOpen
• Subjects: AdS-CFT Correspondence; Classical and Quantum Gravitation; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Conformal and W Symmetry; Conformal Field Theory; Elementary Particles; Field Theories in Lower Dimensions; Form factors; High energy physics; MATHEMATICS AND COMPUTING; Parameters; Partitions; Partitions (mathematics); Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Representations; String Theory; AdS-CFT Correspondence; Field Theories in Lower Dimensions; Conformal and W Symmetry; Conformal Field Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP04(2019)025

A bstract 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 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.