Towards an Asymptotic-Safety Scenario for Chiral Yukawa Systems

We search for asymptotic safety in a Yukawa system with a chiral $U(N_L)_L\otimes U(1)_R$ symmetry, serving as a toy model for the standard-model Higgs sector. Using the functional RG as a nonperturbative tool, the leading-order derivative expansion exhibits admissible non-Ga\ssian fixed-points for $1 \leq N_L \leq 57$ which arise from a conformal threshold behavior induced by self-balanced boson-fermion fluctuations. If present in the full theory, the fixed-point would solve the triviality problem. Moreover, as one fixed point has only one relevant direction even with a reduced hierarchy problem, the Higgs mass as well as the top mass are a prediction of the theory in terms of the Higgs vacuum expectation value. In our toy model, the fixed point is destabilized at higher order due to massless Goldstone and fermion fluctuations, which are particular to our model and have no analogue in the standard model.Comment: 16 pages, 8 figure

Particle-hole fluctuations in the BCS-BEC Crossover

The effect of particle-hole fluctuations for the BCS-BEC crossover is investigated by use of functional renormalization. We compute the critical temperature for the whole range in the scattering length $a$. On the BCS side for small negative $a$ we recover the Gorkov approximation, while on the BEC side of small positive $a$ the particle-hole fluctuations play no important role, and we find a system of interacting bosons. In the unitarity limit of infinite scattering length our quantitative estimate yields $T_c/T_F=0.264$. We also investigate the crossover from broad to narrow Feshbach resonances -- for the later we obtain $T_c/T_F=0.204$ for $a^{-1}=0$. A key ingredient for our treatment is the computation of the momentum dependent four-fermion vertex and its bosonization in terms of an effective bound-state exchange.Comment: 11 pages, 6 figures. Reference adde

Asymptotic safety of simple Yukawa systems

We study the triviality and hierarchy problem of a Z_2-invariant Yukawa system with massless fermions and a real scalar field, serving as a toy model for the standard-model Higgs sector. Using the functional RG, we look for UV stable fixed points which could render the system asymptotically safe. Whether a balancing of fermionic and bosonic contributions in the RG flow induces such a fixed point depends on the algebraic structure and the degrees of freedom of the system. Within the region of parameter space which can be controlled by a nonperturbative next-to-leading order derivative expansion of the effective action, we find no non-Gaussian fixed point in the case of one or more fermion flavors. The fermion-boson balancing can still be demonstrated within a model system with a small fractional flavor number in the symmetry-broken regime. The UV behavior of this small-N_f system is controlled by a conformal Higgs expectation value. The system has only two physical parameters, implying that the Higgs mass can be predicted. It also naturally explains the heavy mass of the top quark, since there are no RG trajectories connecting the UV fixed point with light top masses.Comment: 14 pages, 3 figures, v2: references added, typos corrected, minor numerical correction

Asymptotic Safety, Emergence and Minimal Length

There seems to be a common prejudice that asymptotic safety is either incompatible with, or at best unrelated to, the other topics in the title. This is not the case. In fact, we show that 1) the existence of a fixed point with suitable properties is a promising way of deriving emergent properties of gravity, and 2) there is a sense in which asymptotic safety implies a minimal length. In so doing we also discuss possible signatures of asymptotic safety in scattering experiments.Comment: LaTEX, 20 pages, 2 figures; v.2: minor changes, reflecting published versio

Renormalization Group Flow in Scalar-Tensor Theories. II

We study the UV behaviour of actions including integer powers of scalar curvature and even powers of scalar fields with Functional Renormalization Group techniques. We find UV fixed points where the gravitational couplings have non-trivial values while the matter ones are Gaussian. We prove several properties of the linearized flow at such a fixed point in arbitrary dimensions in the one-loop approximation and find recursive relations among the critical exponents. We illustrate these results in explicit calculations in $d=4$ for actions including up to four powers of scalar curvature and two powers of the scalar field. In this setting we notice that the same recursive properties among the critical exponents, which were proven at one-loop order, still hold, in such a way that the UV critical surface is found to be five dimensional. We then search for the same type of fixed point in a scalar theory with minimal coupling to gravity in $d=4$ including up to eight powers of scalar curvature. Assuming that the recursive properties of the critical exponents still hold, one would conclude that the UV critical surface of these theories is five dimensional.Comment: 14 pages. v.2: Minor changes, some references adde

Probing baryogenesis through the Higgs boson self-coupling

The link between a modified Higgs self-coupling and the strong first-order phase transition necessary for baryogenesis is well explored for polynomial extensions of the Higgs potential. We broaden this argument beyond leading polynomial expansions of the Higgs potential to higher polynomial terms and to nonpolynomial Higgs potentials. For our quantitative analysis we resort to the functional renormalization group, which allows us to evolve the full Higgs potential to higher scales and finite temperature. In all cases we find that a strong first-order phase transition manifests itself in an enhancement of the Higgs self-coupling by at least 50%, implying that such modified Higgs potentials should be accessible at the LHC