On Classification of Fermionic Rational Conformal Field Theories

TL;DR

This paper advances the classification of fermionic rational conformal field theories by analyzing how integrality and modular invariance constrain their parameters, significantly improving existing bootstrap methods.

Contribution

It introduces a novel approach linking integrality of characters to modular invariance, refining the classification of theories with fewer than five characters.

Findings

Constraints on central charge and conformal weights derived

Enhanced classification of fermionic RCFTs with limited characters

Progress in modular bootstrap application for fermionic theories

Abstract

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 $\mathrm{PSL}(2,\mathbb{Z})$. 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.