On the weak-gravity bound for a shift-symmetric scalar field

TL;DR

This paper investigates the weak-gravity bound in a shift-symmetric scalar field system, finding that it may be a truncation artifact and proposing a new criterion based on relevant operators.

Contribution

It provides a detailed analysis of the weak-gravity bound for a shift-symmetric scalar field, challenging previous interpretations and introducing a new perspective based on relevant operators.

Findings

Gaussian fixed point is likely the only viable fixed point without gravity.

Weak-gravity bound may be a truncation artifact.

New notion of weak-gravity bound based on relevant operators.

Abstract

The weak-gravity bound has been discovered in several asymptotically safe gravity-matter systems. It limits the strength of gravitational fluctuations that are compatible with an ultraviolet-complete matter sector, and results from the collision of two partial fixed points of the matter system as a function of the strength of the gravitational interactions. In this paper, we will investigate this mechanism in detail for a shift-symmetric scalar field. First, we will study the fixed point structure of the scalar system without gravity. We find indications that the Gaussian fixed point is the only viable fixed point, suggesting that a weak-gravity bound resulting from the collision of two partial fixed points is a truncation artefact. We will then couple the scalar system to gravity and perform different expansions to track the Gaussian fixed point as gravitational fluctuations become stronger. We also introduce a new notion of the weak-gravity bound that is based on the number of relevant operators.