Speaker
Description
The unitary highest weight representations of integral levels of $\widehat{su}(2)$ current algebra conformal field theories (CFTs) satisfy all properties of a rational CFT (RCFT), but the story is not straightforward at admissible fractional levels. The admissible levels are labelled by two natural coprime numbers $(p\geq 2,u)$ such that the level is $m=p/u-2$.
We show that almost every fractional admissible level $\widehat{su}(2)_m$ current algebra exhibits one or more quasi-character(s). We find three special classes without quasi-characters: the sequence $(p=2,u=2N+1)$, where the admissibility condition is saturated, at positive half-odd integer levels labelled by $(p=2N+3,u=2)$, and an isolated point $(p=3, u=4)$. We also relate the characters of these three classes with characters of RCFTs corresponding to integral levels of $\widehat{su}(2)$ and $\widehat{so}(5)$. The sequence with $u=2$ is quite intriguing and seems to defy most of the usual CFT descriptions (except possibly the$\ log$ CFT). We also report two criteria to eliminate character vectors of the fractional admissible level $\widehat{su}(2)_m$ current algebra at $(p\in prime,u\in prime)$ and $(p, Np-1)$ where $N\in \mathbb{N}$, admitting quasi-characters, as character vectors of an RCFT. Based on 2208.09037.
| Session | Formal Theory |
|---|
