Quasi-Characters in $\widehat{su}(2)$ Current Algebra at Fractional Levels

Sachin Grover

Published 2022-08-18Version 1

We study $\widehat{su}(2)$ representation theory at fractional admissible levels $m=(p/u)-2$, where $p ,u\in\mathbb{N}$ and $(p\geq2, u)$ are coprime. We find that the quasi-characters are quite ubiquitous at these levels. We find three cases without quasi-characters. Two of them are infinite sequences $(p=2,u=2N+1)$, and $(p=2N+3,u=2)$, where $N\in\mathbb{N}$. The third one is an isolated point $(p=3,u=4)$. Among the infinite sequences, the $p=2$ sequence corresponds to threshold cases of admissible levels. The $u=2$ infinite sequence is quite intriguing and seems to defy most of the usual CFT descriptions (except possibly the log-CFT) despite having admissible characters. The isolated point is a curious case with interesting sub-sectors corresponding to unitary CFTs.