K-matrices for 2D conformal field theories

TL;DR

This paper investigates K-matrices in 2D conformal field theories, providing methods to determine them and exploring applications in quantum Hall systems and Kostka polynomials.

Contribution

It introduces techniques for finding K-matrices in 2D CFTs with specific bilinear forms and applies these to various models and physical systems.

Findings

Derived methods for calculating K-matrices in 2D CFTs

Applied techniques to WZW and coset models

Discussed implications for quantum Hall and Kostka polynomials

Abstract

In this paper we examine fermionic type characters (Universal Chiral Partition Functions) for general 2D conformal field theories with a bilinear form given by a matrix of the form K \oplus K^{-1}. We provide various techniques for determining these K-matrices, and apply these to a variety of examples including (higher level) WZW and coset conformal field theories. Applications of our results to fractional quantum Hall systems and (level restricted) Kostka polynomials are discussed.