Abstract
We study the impact of quantum gravity, formulated as a quantum field theory of the metric, on chiral symmetry in a fermionic matter sector. Specifically we address the question of whether metric fluctuations can induce chiral symmetry breaking and bound state formation. Our results based on the functional renormalization group indicate that chiral symmetry is left intact even at strong gravitational coupling. In particular, we found that asymptotically safe quantum gravity where the gravitational couplings approach a non-Gaußian fixed point generically admits universes with light fermions. Our results thus further support quantum gravity theories built on fluctuations of the metric field such as the asymptotic-safety scenario. A study of chiral symmetry breaking through gravitational quantum effects may also serve as a significant benchmark test for other quantum gravity scenarios, since a completely broken chiral symmetry at the Planck scale would not be in accordance with the observation of light fermions in our universe. We demonstrate that this elementary observation already imposes constraints on a generic UV completion of gravity.
Highlights
Any phenomenologically relevant theory of quantum gravity has to satisfy a number of physical requirements
We have investigated the quantum interplay between chiral fermions and metric fluctuations in quantum gravity
In contrast to QCD-like systems, where gluon fluctuations can induce strong fermionic correlations leading to chiral symmetry breaking, metric fluctuations do not support this mechanism in an analogous framework
Summary
Any phenomenologically relevant theory of quantum gravity has to satisfy a number of physical requirements. Our study of the gravitationally-stimulated chiral dynamics is based on a truncation of the full quantum effective action that concentrates on a Fierz-complete basis of chiral fermionic four-point functions in the point-like limit This is motivated by analogous studies in other theories, where such an ansatz provides both for an intuitive as well as quantitatively meaningful approach to chiral symmetry breaking. Gravitational binding which would favor chiral symmetry breaking is compensated by gravitational contributions to anomalous scaling of the fermion interactions Within this minimal truncation, we can conclude that asymptotic safety is well compatible with the existence (and observation) of light fermions despite an interacting UV sector which stimulates fermion self-interactions.
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