We compute the gravitational corrections to the running of couplings in a scalar-fermion system, using the Wilsonian approach. Our discussion is relevant for symmetric as well as for broken scalar phases. We find that the Yukawa and quartic scalar couplings become irrelevant at the Gaussian fixed point.Comment: 5 pages, RevTex, discussion extended, typos corrected, reference added. Published online on PLB

The critical behavior of a relativistic Z 2 -symmetric Yukawa model at zero temperature and density is discussed for a continuous number of fermion degrees of freedom and of spacetime dimensions, with emphasis on the role played by multi-meson exchange in the Yukawa sector. We argue that this should be generically taken into account in studies based on the functional renormalization group, either in four-dimensional high-energy models or in lower-dimensional condensed-matter systems. By means of the latter method, we describe the generation of multi-critical models in less then three dimensions, both at infinite and finite number of flavors. We also provide different estimates of the critical exponents of the chiral Ising universality class in three dimensions for various field contents, from a couple of massless Dirac fermions down to the supersymmetric theory with a single Majorana spinor.

We investigate chiral Higgs-Yukawa models with a non-abelian gauged left-handed sector reminiscent to a sub-sector of the standard model. We discover a new weak-coupling fixed-point behavior that allows for ultraviolet complete RG trajectories which can be connected with a conventional long-range infrared behavior in the Higgs phase. This non-trivial ultraviolet behavior is characterized by asymptotic freedom in all interaction couplings, but a quasi conformal behavior in all mass-like parameters. The stable microscopic scalar potential asymptotically approaches flatness in the ultraviolet, however, with a non-vanishing minimum increasing inversely proportional to the asymptotically free gauge coupling. This gives rise to nonperturbative -though weak-couplingthreshold effects which induce ultraviolet stability along a line of fixed points. Despite the weakcoupling properties, the system exhibits non-Gaußian features which are distinctly different from its standard perturbative counterpart: e.g., on a branch of the line of fixed points, we find linear instead of quadratically running renormalization constants. Whereas the Fermi constant and the top mass are naturally of the same order of magnitude, our model generically allows for light Higgs boson masses. Realistic mass ratios are related to particular RG trajectories with a "walking" mid-momentum regime.