Universal correlators and novel cosets in 2d RCFT

Abstract

The two-character level-1 WZW models corresponding to Lie algebras in the Cvitanović-Deligne series A1, A2, G2, D4, F4, E6, E7 have been argued to form coset pairs with respect to the meromorphic E8,1 CFT. Evidence for this has taken the form of holomorphic bilinear relations between the characters. We propose that suitable 4-point functions of primaries in these models also obey bilinear relations that combine them into current correlators for E8,1, and provide strong evidence that these relations hold in each case. Different cases work out due to special identities involving tensor invariants of the algebra or hypergeometric functions. In particular these results verify previous calculations of correlators for exceptional WZW models, which have rather subtle features. We also find evidence that the intermediate vertex operator algebras A0.5 and E7.5, as well as the three-character A4,1 theory, also appear to satisfy the novel coset relation.