Universal RCFT Correlators from the Holomorphic Bootstrap

TL;DR

This paper develops a universal method using Wronskian differential equations to compute four-point correlation functions in rational conformal field theories, simplifying derivations and extending to complex models like the Baby Monster CFT.

Contribution

It extends the Wronskian differential equations approach to a broad class of CFTs, including non-minimal models, providing a unified framework for correlator computations.

Findings

Derived universal differential equations for conformal blocks.

Re-derived BPZ results for minimal models.

Computed correlators for complex models like Baby Monster CFT.

Abstract

We elaborate and extend the method of Wronskian differential equations for conformal blocks to compute four-point correlation functions on the plane for classes of primary fields in rational (and possibly more general) conformal field theories. This approach leads to universal differential equations for families of CFT's and provides a very simple re-derivation of the BPZ results for the degenerate fields $\phi_{1,2}$ and $\phi_{2,1}$ in the c < 1 minimal models. We apply this technique to compute correlators for the WZW models corresponding to the Deligne-Cvitanovi\'c exceptional series of Lie algebras. The application turns out to be subtle in certain cases where there are multiple decoupled primaries. The power of this approach is demonstrated by applying it to compute four-point functions for the Baby Monster CFT, which does not belong to any minimal series.