Can Quantum Gravity Explain Fermion Masses?

Here is one of the abstracts for the ESQG Conference coming up in Frankfurt, Germany (hat tip Backreaction):

Astrid Eichhorn "Quantum gravity effects on the Higgs-Yukawa sector of the Standard Model" (2016).

After an introduction of the relevant aspects of asymptotically safe quantum gravity, I will focus on first results towards understanding its effects on the Higgs-Yukawa sector of the Standard Model. I will highlight how asymptotically safe quantum gravity can allow us to make predictions about the structure of the matter sector. For instance, exploiting the predictive power of the asymptotic-safety paradigm might allow us to explain the structure of the Higgs-Yukawa sector of the Standard Model. In particular, the asymptotic-safety paradigm could provide a mechanism that generates the difference between the fermion masses.

The underlying conference paper is not available on line at this point, but I suspect that the author may have other publications that explore this concept.   See, for example, her April 2016 paper on the topic:

Astrid Eichhorn, Aaron Held, Jan M. Pawlowski, "Quantum-gravity effects on a Higgs-Yukawa model" (Submitted on 7 Apr 2016 (v1), last revised 13 Sep 2016 (this version, v2))

A phenomenologically viable theory of quantum gravity must accommodate all observed matter degrees of freedom and their properties. Here, we explore whether a toy model of the Higgs-Yukawa sector of the Standard Model is compatible with asymptotically safe quantum gravity. We discuss the phenomenological implications of our result in the context of the Standard Model. We analyze the quantum scaling dimension of the system, and find an irrelevant Yukawa coupling at a joint gravity-matter fixed point. Further, we explore the impact of gravity-induced couplings between scalars and fermions, which are non-vanishing in asymptotically safe gravity.

In particular, the paper proposes a way to determine the Yukawa of the top quark in their toy model, although the result in the particular toy model with a single fermion that they consider 0.4/sqrt(2) is considerable lower than the actual value of ca. 0.996.

Another interesting paper by the same author suggests that quantum gravity may impose a maximum number of fundamental fermions and Higgs bosons per gauge field in the theory:

Pietro Donà, Astrid Eichhorn, Roberto Percacci, "Matter matters in asymptotically safe quantum gravity" (Submitted on 12 Nov 2013 (v1), last revised 15 Feb 2014 (this version, v3)).

We investigate the compatibility of minimally coupled scalar, fermion and gauge fields with asymptotically safe quantum gravity, using nonperturbative functional Renormalization Group methods. We study d=4,5 and 6 dimensions and within certain approximations find that for a given number of gauge fields there is a maximal number of scalar and fermion degrees of freedom compatible with an interacting fixed point at positive Newton coupling. The bounds impose severe constraints on grand unification with fundamental Higgs scalars. Supersymmetry and universal extra dimensions are also generally disfavored. The standard model and its extensions accommodating right-handed neutrinos, the axion and dark-matter models with a single scalar are compatible with a fixed point.