On classification of fermionic rational conformal field theories

A bstract We systematically study how the integrality of the conformal characters shapes the space of fermionic rational conformal field theories in two dimensions. The integrality suggests that conformal characters on torus with a given choice of spin structures should be invariant under a principa...

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Bibliographic Details
Published in:The journal of high energy physics 2023-02, Vol.2023 (2), p.79-32, Article 79
Main Authors: Duan, Zhihao, Lee, Kimyeong, Lee, Sungjay, Li, Linfeng
Format: Article
Language:English
Subjects:
Anyons
Classical and Quantum Gravitation
Classification
Conformal and W Symmetry
Critical phenomena
Elementary Particles
Field Theories in Lower Dimensions
High energy physics
Phase transitions
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Scale and Conformal Symmetries
Spin structure
Statistical methods
String Theory
Subgroups
Symmetry
Toruses
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Summary:A bstract We systematically study how the integrality of the conformal characters shapes the space of fermionic rational conformal field theories in two dimensions. The integrality suggests that conformal characters on torus with a given choice of spin structures should be invariant under a principal congruence subgroup of PSL(2 , ℤ). The invariance strongly constrains the possible values of the central charge as well as the conformal weights in both Neveu-Schwarz and Ramond sectors, which improves the conventional holomorphic modular bootstrap method in a significant manner. This allows us to make much progress on the classification of fermionic rational conformal field theories with the number of independent characters less than five.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP02(2023)079