Universal Correlators and Novel Cosets in 2d RCFT

TL;DR

This paper explores new bilinear relations among 2d RCFT characters, revealing coset structures and correlator identities that extend understanding of exceptional WZW models and propose novel intermediate vertex operator algebras.

Contribution

It introduces bilinear relations for 4-point functions in specific RCFTs, confirming coset pairings and uncovering new algebraic structures beyond previous character-based evidence.

Findings

Bilinear relations hold for 4-point functions in studied models

Verification of correlator calculations for exceptional WZW models

Evidence for new intermediate vertex operator algebras

Abstract

The two-character level-1 WZW models corresponding to Lie algebras in the Cvitanovi\'c-Deligne series $A_1,A_2,G_2,D_4,F_4,E_6,E_7$ have been argued to form coset pairs with respect to the meromorphic $E_{8,1}$ 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 $E_{8,1}$, 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 A$_{0.5}$ and E$_{7.5}$, as well as the three-character A$_{4,1}$ theory, also appear to satisfy the novel coset relation.