Renormalization group effects in the conformal sector of 4d quantom gravity with matter

TL;DR

This paper explores how gravitational effects influence the behavior of quantum field theories, specifically examining beta functions and coupling constants in models involving 2D Liouville theory and 4D quantum gravity with matter.

Contribution

It introduces the concept of gravitationally dressed beta functions in the context of 2D and 4D theories, highlighting potential impacts on effective potentials and gauge coupling running.

Findings

Gravitational dressing affects the minimum of the effective potential.

Running of the gauge coupling is influenced by gravitational effects.

Proposes a framework for incorporating gravity into quantum field theory beta functions.

Abstract

We discuss the ``gravitationally dressed'' beta functions in the Gross--Neveu model interacting with 2d Liouville theory and in $SU(N)$ gauge theory interacting with the conformal sector of 4d quantum gravity. Among the effects that we suggest may feel the gravitational dressing are the minimum of the effective potential and the running of the gauge coupling.