On the S-matrix of Liouville theory

TL;DR

This paper computes the S-matrix for Liouville theory's chiral sectors using a novel one-dimensional field theory approach, linking semiclassical amplitudes with quantum scattering, and validates results through explicit loop diagram comparisons.

Contribution

It introduces a new method to derive the Liouville S-matrix from a non-local 1D field theory and demonstrates its consistency with existing approaches.

Findings

Explicit loop diagrams match other S-matrix computation methods.

The action is shown to be the Legendre transform of the generating function.

The approach clarifies the relation between asymptotic fields and scattering amplitudes.

Abstract

The S-matrix for each chiral sector of Liouville theory on a cylinder is computed from the loop expansion of correlation functions of a one-dimensional field theory on a circle with a non-local kinetic energy and an exponential potential. This action is the Legendre transform of the generating function of semiclassical scattering amplitudes. It is derived from the relation between asymptotic in- and out-fields. Its relevance for the quantum scattering process is demonstrated by comparing explicit loop diagrams computed from this action with other methods of computing the S-matrix, which are also developed.