Liouville theory without an action

TL;DR

This paper demonstrates that crossing symmetry in Liouville conformal field theory alone can determine the theory's structure constants and solve it without relying on the traditional action-based approach.

Contribution

It reveals that crossing symmetry contains sufficient information to solve Liouville theory without the action, under certain assumptions.

Findings

Crossing symmetry determines structure constants non-perturbatively.

Liouville theory can be solved without the action.

The approach reproduces known structure constants.

Abstract

We show that the crossing symmetry of the four-point function in the Liouville conformal field theory on the sphere contains more information than what was hitherto considered. Under certain assumptions, it provides the special structure constants that were previously computed perturbatively and allows to solve the theory without using the Liouville interaction.