Pseudoconformal field theory at the "wrong level"

TL;DR

This paper explores pseudoaffine theories with fractional levels, specifically analyzing an SU(2) case with q=2, and computes spectra of minimal models, revealing fusion properties similar to affine theories.

Contribution

It introduces and analyzes pseudoaffine theories at fractional levels, including a detailed case study of SU(2) with q=2, and computes their spectra.

Findings

Fusion rules resemble affine theories

Spectra of minimal models are explicitly calculated

Identifies 'forbidden' fractional levels with meaningful structure

Abstract

Pseudoaffine theories are characterized by formal replacement of the level to the fractional number: $k\to\frac{k}{q}$, where $q$ is integer strange to $k(g+k)$ ($g$ - dual Coxeter number). An example of "forbidden" $q$ is considered (SU(2), $q=2$). The fusions of obtained theory are similar to the affine ones. Spectra of minimal models are calculated.