Abstract
We study the impact of quantum gravity on a system of chiral fermions that are charged under an Abelian gauge group. Under the impact of quantum gravity, a finite value of the gauge coupling could be generated and in turn drive four-fermion interactions to criticality. We find indications that the gravity-gauge-fermion interplay protects the lightness of fermions for a large enough number of fermions. On the other hand, for a smaller number of fermions, chiral symmetry may be broken, which would be in tension with the observation of light fermions.
Highlights
Light fermions as a test of quantum gravityThe observation of light fermions in our universe motivates studies of the interplay of chiral fermions with quantum gravity
We study the impact of quantum gravity on a system of chiral fermions that are charged under an Abelian gauge group
This is in contrast to non-Abelian gauge theories, where chiral symmetry breaking in was studied with the functional Renormalization Group (FRG) in [23,24,25,26,27,28,29,30]
Summary
The observation of light fermions in our universe motivates studies of the interplay of chiral fermions with quantum gravity. Despite the attractive nature of the classical gravitational interaction, quantum gravity fluctuations do not appear to lead to bound-state formation and chiral symmetry breaking This is in contrast to non-Abelian gauge theories, where chiral symmetry breaking in was studied with the FRG in [23,24,25,26,27,28,29,30]. As a large enough value of the gauge interaction results in chiral symmetry breaking [47,48,49,50,51,52], a competition between gravitational and effects of the gauge field can be expected Such an interplay could result in a lower bound on the number of fermions. As the underlying reason for the existence of three generations in the Standard Model is unknown, it is fascinating to understand whether the number of generations is tied to the lightness of fermions, see [40]
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