Smoothness of correlation functions in Liouville Conformal Field Theory

TL;DR

This paper proves the smoothness of correlation functions in probabilistic Liouville Conformal Field Theory, advancing the understanding of their mathematical properties and supporting the conformal bootstrap predictions.

Contribution

It establishes the smoothness of correlation functions in probabilistic Liouville CFT, a key step towards verifying higher Ward identities and BPZ equations.

Findings

Correlation functions are proven to be smooth functions.

Supports the conformal bootstrap approach predictions.

Progress towards proving higher Ward identities and BPZ equations.

Abstract

In this article we prove smoothness of the correlation functions in probabilistic Liouville Conformal Field Theory. Our result is a step towards proving that the correlation functions satisfy the higher Ward identities and the higher BPZ equations, predicted by the Conformal Bootstrap approach to Conformal Field Theory.