Ward Identities for Affine-Virasoro Correlators

TL;DR

This paper derives a hierarchy of non-linear Ward identities for affine-Virasoro correlators, extending the Knizhnik-Zamolodchikov equations, and provides solutions for coset constructions using matrix factorization.

Contribution

It introduces a new hierarchy of Ward identities for affine-Virasoro correlators and demonstrates their solution in coset models with matrix factorization.

Findings

Derived non-linear Ward identities generalizing KZ equations.

Solved equations explicitly for coset models.

Coset correlators satisfy linear PDEs with known solutions.

Abstract

Generalizing the Knizhnik-Zamolodchikov equations, we derive a hierarchy of non-linear Ward identities for affine-Virasoro correlators. The hierarchy follows from null states of the Knizhnik-Zamolodchikov type and the assumption of factorization, whose consistency we verify at an abstract level. Solution of the equations requires concrete factorization ans\"atze, which may vary over affine-Virasoro space. As a first example, we solve the non-linear equations for the coset constructions, using a matrix factorization. The resulting coset correlators satisfy first-order linear partial differential equations whose solutions are the coset blocks defined by Douglas.