On parity functions in conformal field theories

TL;DR

This paper explores the properties of parity functions in rational conformal field theories, especially those linked to affine Lie algebras, and discusses their implications for modular invariance.

Contribution

It provides new formulas for parity functions related to affine Lie algebras and analyzes their role in the modular invariance problem.

Findings

Derived two efficient formulas for parity functions of affine Lie algebras

Linked Galois properties to modular transformation behaviors

Discussed implications for modular invariance in conformal field theories

Abstract

We examine general aspects of parity functions arising in rational conformal field theories, as a result of Galois theoretic properties of modular transformations. We focus more specifically on parity functions associated with affine Lie algebras, for which we give two efficient formulas. We investigate the consequences of these for the modular invariance problem.