http://arxiv.org/abs/1911.06100
We investigate the shape of the effective potential for scalar fields at and near the ultraviolet fixed point of asymptotically safe quantum gravity. We find scaling solutions with a completely flat potential and vanishing gauge and Yukawa couplings. Nonvanishing gauge couplings can induce spontaneous symmetry breaking due to a potential minimum at nonzero field values. In contrast, Yukawa couplings to fermions tend to stabilize a minimum at zero field values. A nonminimal coupling between the scalar field and gravity is associated to a field-dependent effective Planck mass. It can induce spontaneous symmetry breaking. In general, nonzero gauge, Yukawa or nonminimal couplings prevent the scaling potential to be completely flat. For the standard model coupled to asymptotically safe quantum gravity the non-minimal Higgs-curvature coupling is bound to be small, $\xi_{\infty} \lesssim 10^{-3}$, in contrast to large values $\xi_{\infty} > 1$ often assumed for Higgs inflation. We also discuss small modifications of the predicted value for the top quark mass due to nonzero gauge and Yukawa couplings.
C. Wetterich
Fri, 15 Nov 19
8/73
Comments: 37 pages, 26 figures
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