Dangerous Liouville Wave -- exactly marginal but non-conformal deformation

TL;DR

This paper presents a scale invariant yet non-conformal quantum field theory constructed from Liouville theory coupled with free scalars, highlighting a non-trivial example with potential implications for super-critical string theory.

Contribution

It introduces a novel exactly marginal deformation of Liouville theory that results in a non-conformal but scale invariant quantum field theory, expanding understanding of such models.

Findings

Demonstrates non-vanishing trace of energy-momentum tensor

Uses quantum Schwinger-Dyson equations for analysis

Discusses implications for super-critical string theory

Abstract

We give a non-trivially interacting field theory example of scale invariant but non-conformal field theory. The model is based on the exactly solvable Liouville field theory coupled with free scalars deformed by an exactly marginal operator. We show non-vanishing of the trace of the energy-momentum tensor by using the quantum Schwinger-Dyson equation for the Liouville field theory, which is a sophistication of the quantum higher equations of motion for the Liouville field theory introduced by Alyosha Zamolodchikov. Possibly dangerous implications for the super-critical string theory will be discussed.