Constraints on discrete global symmetries in quantum gravity

TL;DR

This paper investigates the viability of discrete global symmetries in quantum gravity, finding constraints within asymptotic safety and potential roles in effective field theories for mass hierarchy generation.

Contribution

It provides evidence that certain discrete symmetries cannot exist in asymptotically safe quantum gravity, contrasting with their possible emergence in effective-field-theory frameworks.

Findings

Discrete symmetries with n>4 are not realizable in asymptotic safety.

Effective-field-theory approaches can feature such symmetries.

Potential mechanism for infrared mass hierarchies without fine-tuning.

Abstract

The question whether global symmetries can be realized in quantum-gravity-matter-systems has far-reaching phenomenological consequences. Here, we collect evidence that within an asymptotically safe context, discrete global symmetries of the form $\mathbb{Z}_n$, $n>4$, cannot be realized in a near-perturbative regime. In contrast, an effective-field-theory approach to quantum gravity might feature such symmetries, providing a mechanism to generate mass hierarchies in the infrared without the need for additional fine-tuning.