The beta functions of a scalar theory coupled to gravity

TL;DR

This paper investigates how gravity influences the behavior of a scalar field theory at energies below the Planck scale by calculating gravitational corrections to its renormalization group flow.

Contribution

It provides the first detailed calculation of gravitational corrections to the beta functions and anomalous dimensions in a scalar field theory using Wilson's renormalization group approach.

Findings

Gravitational effects modify the scalar field's beta functions.

Threshold effects are significant in the renormalization group analysis.

Results are relevant for understanding quantum gravity's impact on matter fields.

Abstract

We study a scalar field theory coupled to gravity on a flat background, below Planck's energy. Einstein's theory is treated as an effective field theory. Within the context of Wilson's renormalization group, we compute gravitational corrections to the beta functions and the anomalous dimension of the scalar field, taking into account threshold effects.