Classification of Unitary RCFTs with Two Primaries and Central Charge Less Than 25

Abstract

We classify all two-dimensional, unitary, rational conformal field theories with two primaries, central charge $c<25$, and arbitrary Wronskian index. In mathematical parlance, we classify all strongly regular vertex operator algebras (VOAs) with central charge $c<25$ and exactly two simple modules. We find that any such theory is either one of the Mathur-Mukhi-Sen (MMS) theories ${\mathsf{A}}_{1,1}$, ${\mathsf{G}}_{2,1}$, ${\mathsf{F}}_{4,1}$, or ${\mathsf{E}}_{7,1}$, or it is a coset of a chiral algebra with one primary operator (also known as a holomorphic VOA) by such an MMS theory. By leveraging existing results on the classification of holomorphic VOAs, we are able to explicitly enumerate all of the aforementioned cosets and compute their characters. This leads to 123 theories, most of which are new. We emphasize that our work is a bona fide classification of RCFTs, not just of characters. Our techniques are general, and we argue that they offer a promising strategy for classifying chiral algebras with low central charge beyond two primaries.

arXiv comment62 pages, 7 tables, 1 figure. Several typos corrected. References updated

References in corpus (30)

• Infinite Chiral Symmetry in Four Dimensions
• TFT construction of RCFT correlators I: Partition functions
• Meromorphic c=24 Conformal Field Theories
• Correspondences of ribbon categories
• Vertex operator algebras, Higgs branches, and modular differential equations
• Framed vertex operator algebras, codes and the moonshine module
• The Frobenius-Schur indicator in Conformal Field Theory
• Braided tensor categories and extensions of vertex operator algebras
• Congruence Property In Conformal Field Theory
• Construction and Classification of Holomorphic Vertex Operator Algebras
• The kernel of the modular representation and the Galois action in RCFT
• The intermediate vertex subalgebras of the lattice vertex operator algebras
• Two-dimensional RCFT's without Kac-Moody symmetry
• Quadratic spaces and holomorphic framed vertex operator algebras of central charge 24
• Gluing vertex algebras
• Conformal characters and the modular representation
• Conformal Field Theories with Sporadic Group Symmetry
• Dimension Formulae and Generalised Deep Holes of the Leech Lattice Vertex Operator Algebra
• Schellekens' List and the Very Strange Formula
• Classifying three-character RCFTs with Wronskian Index equalling $0$ or $2$
• Needles in a haystack: An algorithmic approach to the classification of 4d $\mathcal{N}=2$ SCFTs
• Galois Symmetry Induced by Hecke Relations in Rational Conformal Field Theory and Associated Modular Tensor Categories
• Systematic Orbifold Constructions of Schellekens' Vertex Operator Algebras from Niemeier Lattices
• On classification of extremal non-holomorphic conformal field theories
• Curiosities above c = 24
• Traces of Singular Moduli and Moonshine for the Thompson Group
• Cosets of Meromorphic CFTs and Modular Differential Equations
• Dimension Formulae in Genus Zero and Uniqueness of Vertex Operator Algebras
• The Umbral Moonshine Module for the Unique Unimodular Niemeier Root System
• Classification of extremal vertex operator algebras with two simple modules

Cited by in corpus (9)

• Remarks on Boundaries, Anomalies, and Noninvertible Symmetries
• Holographic theory for continuous phase transitions -- the emergence and symmetry protection of gaplessness
• Bosonic Rational Conformal Field Theories in Small Genera, Chiral Fermionization, and Symmetry/Subalgebra Duality
• Non-Chiral Vertex Operator Algebra Associated To Lorentzian Lattices And Narain CFTs
• Two approaches to the holomorphic modular bootstrap
• Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs
• Three Dimensional Topological Field Theories and Nahm Sum Formulas
• Quasi-Characters in $\widehat{su(2)}$ Current Algebra at Fractional Levels
• Rényi entropy of single-character CFTs on the torus