The Two-exponential Liouville Theory and the Uniqueness of the Three-point Function

TL;DR

This paper demonstrates the unique determination of three-point function coefficients in the two-exponential Liouville theory using path integral invariance and self-consistency, aligning with conformal bootstrap results.

Contribution

It establishes the uniqueness of three-point function coefficients in the two-exponential Liouville theory through a novel approach based on path integral invariance.

Findings

Coefficients of three-point functions are uniquely determined.

Results agree with conformal bootstrap methods.

Reflection symmetry and parameter relationships are derived.

Abstract

It is shown that in the two-exponential version of Liouville theory the coefficients of the three-point functions of vertex operators can be determined uniquely using the translational invariance of the path integral measure and the self-consistency of the two-point functions. The result agrees with that obtained using conformal bootstrap methods. Reflection symmetry and a previously conjectured relationship between the dimensional parameters of the theory and the overall scale are derived.