The classification of chiral WZW models by $H_{+}^4(BG,\mathbb{Z})$

Abstract

We axiomatize the defining properties of chiral WZW models. We show that such models are in almost bijective correspondence with pairs $(G,k)$, where $G$ is a connected Lie group and $k\in H_{+}^4(BG,\mathbb{Z})$ is a degree four cohomology class subject to a certain positivity condition. We find a couple extra models which satisfy all the defining properties of chiral WZW models, but which don't come from pairs $(G,k)$ as above. The simplest such model is the simple current extension of the affine VOA $E_8\times E_8$ at level $(2,2)$ by the group ${\mathbb{Z}}_2$.

25 pages; added a section about WZW conformal nets

References in corpus (4)

• Simple current extensions beyond semi-simplicity
• From vertex operator algebras to conformal nets and back
• Transgressive loop group extensions
• On the unitary structures of vertex operator superalgebras

Cited by in corpus (1)

• Third Homology of some Sporadic Finite Groups