On The Characters of Parafermionic Field Theories

TL;DR

This paper investigates parafermionic field theories derived from Lie algebra cosets, providing a universal Rogers-Ramanujan type identity for their characters, verified across multiple cases using recursive multiplicity calculations.

Contribution

It introduces a general identity for parafermionic characters applicable to all Lie algebra cosets and levels, unifying known results and expanding the theoretical framework.

Findings

Derived a universal Rogers-Ramanujan type identity for characters

Verified the identity for various algebras and levels using Kac formula

Unified existing results and discovered new character identities

Abstract

We study cosets of the type $H_l/U(1)^r$, where $H$ is any Lie algebra at level $l$ and rank $r$. These theories are parafermionic and their characters are related to the string functions, which are generating functions for the multiplicities of weights in the affine representations. An identity for the characters is described, which apply to all the algebras and all the levels. The expression is of the Rogers Ramanujan type. We verify this conjecture, for many algebras and levels, using Freudenthal Kac formula, which calculates the multiplicities in the affine representations, recursively, up to some grade. Our conjecture encapsulates all the known results about these string functions, along with giving a vast wealth of new ones.