Bootstrapping Fermionic Rational CFTs with Three Characters

Abstract

Recently, the modular linear differential equation (MLDE) for level-two congruence subgroups ${\Gamma }_{\theta },{\Gamma }^0(2)$ and ${\Gamma }_0(2)$ of ${\text{SL}}_2(\mathbb{Z})$ was developed and used to classify the fermionic rational conformal field theories (RCFT). Two character solutions of the second-order fermionic MLDE without poles were found and their corresponding CFTs are identified. Here we extend this analysis to explore the landscape of three character fermionic RCFTs obtained from the third-order fermionic MLDE without poles. Especially, we focus on a class of the fermionic RCFTs whose Neveu-Schwarz sector vacuum character has no free-fermion currents and Ramond sector saturates the bound $h^{\text{R}}\ge \frac{c}{24}$, which is the unitarity bound for the supersymmetric case. Most of the solutions can be mapped to characters of the fermionized WZW models. We find the pairs of fermionic CFTs whose characters can be combined to produce $K(\tau )$, the character of the $c=12$ fermionic CFT for ${\text{Co}}_0$ sporadic group.

arXiv comment56 pages, 11 tables

References in corpus (21)

• Meromorphic c=24 Conformal Field Theories
• A theory of 2+1D bosonic topological orders
• Fermionic Modular Categories and the 16-fold Way
• A Web of 2d Dualities: ${\mathbf{Z}}_2$ Gauge Fields and Arf Invariants
• Fermionic minimal models
• On 2d Conformal Field Theories with Two Characters
• Fermionic CFTs and classifying algebras
• Two-dimensional RCFT's without Kac-Moody symmetry
• Selbstduale Vertexoperatorsuperalgebren und das Babymonster (Self-dual Vertex Operator Super Algebras and the Baby Monster)
• Towards a Classification of Two-Character Rational Conformal Field Theories
• Holomorphic modular bootstrap revisited
• Two More Fermionic Minimal Models
• Conformal Field Theories with Sporadic Group Symmetry
• On the classification of fusion rings
• Classifying three-character RCFTs with Wronskian Index equalling $0$ or $2$
• Simple-current algebra constructions of 2+1D topological orders
• Classification of RCFT from Holomorphic Modular Bootstrap: A Status Report
• Classification of some vertex operator algebras of rank 3
• Monster Anatomy
• Duality Defect of the Monster CFT
• Emergent Supersymmetry on the Edges

Cited by in corpus (10)

• Bosonic Rational Conformal Field Theories in Small Genera, Chiral Fermionization, and Symmetry/Subalgebra Duality
• 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
• Surface defects, flavored modular differential equations and modularity
• Hecke Relations, Cosets and the Classification of 2d RCFTs
• On Classification of Fermionic Rational Conformal Field Theories
• Meromorphic Cosets and the Classification of Three-Character CFT
• New meromorphic CFTs from cosets
• Modular extension of topological orders from congruence representations
• Two approaches to the holomorphic modular bootstrap