On a relation between Liouville field theory and a two component scalar field theory passing through the random walk

TL;DR

This paper introduces a transformation that simplifies exponential potentials, demonstrating how Liouville field theory can be mapped into a polynomial scalar field theory with an additional massive vector field.

Contribution

It presents a novel transformation linking Liouville theory to a polynomial scalar and vector field theory, simplifying the analysis of non-polynomial potentials.

Findings

Liouville theory mapped to polynomial scalar-vector field theory

Transformation simplifies exponential potentials

Potential applications in quantum field theory analysis

Abstract

In this work it is proposed a transformation which is useful in order to simplify non-polynomial potentials given in the form of an exponential. As an application, it is shown that the quantum Liouville field theory may be mapped into a field theory with a polynomial interaction between two scalar fields and a massive vector field.