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We investigate whether quantum gravity fluctuations can break chiral symmetryfor fermions that are charged under a $U(1)$ and an $SU(N_\text{c})$ gaugesymmetry and thus closely resemble Standard-Model fermions. Unbroken chiralsymmetry in the quantum-gravity regime is a necessary prerequisite to recoverthe Standard Model from a joint gravity-matter theory; if chiral symmetry isbroken by quantum gravity, fermions cannot generically be much lighter than thePlanck mass and the theory is ruled out. To answer this, we work in aFierz-complete basis of four-fermion interactions and explore whether they aredriven to criticality.  We discover that the interplay of quantum gravity with the non-Abelian gaugetheory results in chiral symmetry breaking, because gravitational and gaugefield fluctuations act together to produce bound states.  Chiral symmetry breaking is triggered by four-fermion channels that firstappear when non-Abelian charges are introduced and that become critical if thenon-Abelian symmetry is gauged. Extrapolating our result to the Standard Modelfermions, we conjecture that the non-Abelian gauge coupling, Abelian gaugecoupling and Newton coupling are all bounded from above, if Standard Modelfermions are to remain much lighter than the Planck mass.  In contrast, fermions that are charged under a global non-Abelian group canremain light for arbitrarily large values of the Newton coupling. We find thatdifferent chiral symmetries are emergent at low energies, depending on thestrength of the gravitational coupling. This is an example of fixed points withdifferent degrees of enhanced global symmetry trading stability in fixed-pointcollisions driven by gravitational fluctuations.

Light fermions in color: why the quark mass is not the Planck mass