Abstract
We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works (Christiansen et al., Phys Rev D 92:121501, 2015; Meibohm et al., Phys Rev D 93:084035, 2016), concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models. We find strong evidence that this feature is independent of the number of fermion fields. This finding suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions.
Highlights
Finding a well-defined theory for quantum gravity is a major challenge of modern theoretical physics
We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group
The present analysis which is based on the previous works (Christiansen et al, Phys Rev D 92:121501, 2015; Meibohm et al, Phys Rev D 93:084035, 2016), concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models
Summary
Finding a well-defined theory for quantum gravity is a major challenge of modern theoretical physics. The asymptotic safety scenario [3] is a promising approach towards a solution to this problem It relies on the description of quantum gravity in terms of a local, fundamental quantum field theory of the metric. In Non-Abelian gauge theories coupled to matter, the gluon-induced fermion correlations are responsible for the generation of fermion masses at low energies In these theories, the gauge coupling becomes large at low energies and eventually exceeds a critical value. Gravity becomes strongly interacting in the ultraviolet within the asymptotic safety scenario This raises the question whether there exists a critical gravitational coupling for which chiral symmetry is broken dynamically at high energies. Our study implies that metric gravity and the asymptotic safety scenario stay consistent under the inclusion of an arbitrary number of fermions with a point-like 4-fermion interaction
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