Characters for Coset Conformal Field Theories

TL;DR

This paper derives explicit character formulas for coset conformal field theories by solving the Kac-Moody branching equations, providing new insights into their structure and primary field weights.

Contribution

It introduces explicit character formulas for coset CFTs and presents an example outside the identification current method framework.

Findings

Explicit formulas for coset characters derived

Determination of conformal weight shifts for primary fields

An example of a coset CFT not describable by identification currents

Abstract

We solve the Kac-Moody branching equation to obtain explicit formulae for the characters of coset conformal field theories and then apply these to specific examples to determine the integer shift of the conformal weights of primary fields. We also present an example of coset conformal field theory which cannot be described by the identification current method.