WZNW Models from Non-Standard Bilinear Forms

TL;DR

This paper explores WZNW models constructed from nonstandard bilinear forms, revealing the existence of irrational conformal field theories and analyzing the unitarity of Kac-Moody representations in noncompact groups.

Contribution

It introduces new algebraic and analytical methods to study WZNW models with nonstandard bilinear forms, including the discovery of irrational CFTs at integer levels.

Findings

Existence of irrational CFTs at integer levels

Kac-Moody representations are nonunitary for certain noncompact groups

Multiple analytical approaches applied to the models

Abstract

We study the WZNW models based on nonstandard bilinear forms. We approach the problem from algebraic, perturbative and functional exact methods. It is shown that even in the case of integer $k$ we can find irrational CFT's. We prove that when the base group is noncompact with nonabelian maximal compact subgroup, the Kac-Moody representations are nonunitary.