Quadratic gravity in analogy to quantum chromodynamics: Light fermions in its landscape

TL;DR

This paper explores the analogy between quadratic gravity and quantum chromodynamics, investigating whether gravity can induce chiral symmetry breaking, and finds that it does not in a non-perturbative regime, supporting the analogy's viability.

Contribution

It provides the first non-perturbative analysis of chiral symmetry breaking in quadratic gravity using functional renormalization group methods.

Findings

Gravity does not trigger chiral symmetry breaking in the studied regime.

The analogy between quadratic gravity and QCD remains phenomenologically viable.

Single-flavor case exhibits particular features that are discussed.

Abstract

We investigate a non-perturbative approach to quantum gravity built in terms of analogies between quadratic gravity and quantum chromodynamics. This approach is based on a conjectured phase transition between quadratic gravity in the trans-Planckian regime and an effective field theory, with general relativity as the leading-order term, below the Planck scale. We point out that not all aspects of the analogy between quadratic gravity and quantum chromodynamics are desired. A possible mechanism of chiral symmetry breaking driven by quantum gravity fluctuations could make this setup incompatible with our observed Universe. Here, we put forward a first investigation of chiral symmetry breaking in the context of quadratic gravity. We find indication that gravity, despite being an attractive force, does not trigger chiral symmetry breaking in a non-perturbative regime. This result is based on a (functional) renormalization group analysis of four-fermion interactions coupled to quadratic gravity. We also comment on the particularities associated with the single-flavor case. In summary, the analogy between quadratic gravity and chromodynamics passes this first phenomenological viability test.