C. Wetterich

Cosmology and the Fate of Dilatation Symmetry

Abstract We discuss the cosmological constant problem in the light of dilatation symmetry and its possible anomaly. For dilatation symmetric quantum theories realistic asymptotic cosmology is obtained provided the effective potential has a nontrivial minimum. For theories with dilatation anomaly one needs as a nontrivial “cosmon condition” that the energy-momentum tensor in the vacuum is purely anomalous. Such a condition is related to the short distance renormalization group behaviour of the fundamental theory. Observable deviations from the standard hot big bang cosmology are possible.

Exact evolution equation for the effective potential

Abstract We derive a new exact evolution equation for the scale dependence of an effective action. The corresponding equation for the effective potential permits a useful truncation. This allows one to deal with the infrared problems of theories with massless modes in less than four dimensions which are relevant for the high temperature phase transition in particle physics or the computation of critical exponents in statistical mechanics.

Proton Lifetime and Fermion Masses in an SO(10) Model

Some consequences of an SO(10) gauge theory which breaks down to SU(3)c × U(1)e.m. via SU(4)c × SU(2)L × SU(2)R are presented. These include: (i) A proton lifetime estimate of (1–20) × 1031 yr. (ii) Mass relations involving quarks and charged leptons. The explanation of the violation of the asymptotic SU(5) relation me = md is linked to the new intermediate mass scale in SO(10). The top quark mass is estimated to be 20 ± 2 GeV at the toponium mass. (iii) The possibility of a fourth generation (ντ′, τ′, b′, t′) with mτ′ ≅ 17–35 GeV, mb′ ⋍ 42–118 GeV and mt′ ⋍ 150–230 GeV. (iv) Heaviest neutrino mass in the 1–10 eV range. In addition, the masses of the superheavy neutrinos are of order 5 × 1012 − 5 × 1013 GeV. (v) Neutron-antineutron oscillations with τnn > 1038 yr.

Non-perturbative renormalization flow in quantum field theory and statistical physics

Abstract We review the use of an exact renormalization group equation in quantum field theory and statistical physics. It describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. Non-perturbative solutions follow from approximations to the general form of the coarse-grained free energy or effective average action. They interpolate between the microphysical laws and the complex macroscopic phenomena. Our approach yields a simple unified description for O ( N )-symmetric scalar models in two, three or four dimensions, covering in particular the critical phenomena for the second-order phase transitions, including the Kosterlitz–Thouless transition and the critical behavior of polymer chains. We compute the aspects of the critical equation of state which are universal for a large variety of physical systems and establish a direct connection between microphysical and critical quantities for a liquid–gas transition. Universal features of first-order phase transitions are studied in the context of scalar matrix models. We show that the quantitative treatment of coarse graining is essential for a detailed estimate of the nucleation rate. We discuss quantum statistics in thermal equilibrium or thermal quantum field theory with fermions and bosons and we describe the high-temperature symmetry restoration in quantum field theories with spontaneous symmetry breaking. In particular, we explore chiral symmetry breaking and the high-temperature or high-density chiral phase transition in quantum chromodynamics using models with effective four-fermion interactions.

Neutrino Masses and the Scale of B-L Violation

Abstract A systematic study of neutrino masses in models with local B - L symmetry is presented. The observed SU(4) c violation in fermion masses, which is necessary to explain why m e is not equal m d , is related to the scale of B - L violation. An alternative approach uses renormalization group methods to determine this scale. The heaviest neutrino mass is predicted to be 0.1–50 eV in the case of four fermion generations. Two different generation patterns for neutrino masses are found, one predicting large mixing between ν e and ν μ (and eventually ν τ ) and the other predicting leptonic mixing angles of the same order as quark mixing angles.

Effective average action for gauge theories and exact evolution equations

Abstract We propose a new nonperturbative evolution equation for Yang-Mills theories. It describes the scale dependence of an effective action. The running of the nonabelian gauge coupling in arbitrary dimension is computed.

Average action and the renormalization group equations

Abstract We formulate an effective action Γ k for averages of fields taken within a volume of size k −d. In contrast to the block-spin approach on the lattice we work in continuous (euclidean) space, preserving all symmetries. We establish how expectation values of operators with momenta smaller than k can be computed from Γ k. The average action at different scales is related by an exact renormalization group equation. We apply these ideas to the N-component φ 4 theory in the spontaneously broken phase and derive the one-loop renormalization group equations for the average potential. The average potential becomes convex as k → 0.

Asymptotic safety of gravity and the Higgs boson mass

There are indications that gravity is asymptotically safe. The Standard Model (SM) plus gravity could be valid up to arbitrarily high energies. Supposing that this is indeed the case and assuming that there are no intermediate energy scales between the Fermi and Planck scales we address the question of whether the mass of the Higgs boson mH can be predicted. For a positive gravity induced anomalous dimension Aλ > 0 the running of the quartic scalar self interaction λ at scales beyond the Planck mass is determined by a fixed point at zero. This results in mH = mmin = 126 GeV, with only a few GeV uncertainty. This prediction is independent of the details of the short distance running and holds for a wide class of extensions of the SM as well. For Aλ 0 is favored by explicit computations existing in the literature.

Critical Exponents from the Effective Average Action

Abstract We compute the critical behaviour of three-dimensional scalar theories using a new exact non-perturbative evolution equation. Our values for the critical exponents and other universal constants agree well with previous precision estimates. The evolution equation describes the scale dependence of the effective average action (coarse-grained effective action). It is not restricted to critical phenomena and can be used in the presence of massless (Goldstone) modes dealing successfully with the infrared problems. Our results establish the viability of our method for precise computations in a non-perturbative context.

Cosmologies with variable Newton's “constant”

Abstract We discuss cosmologies where the Planck length is not a fundamental constant but rather evolves with time. The dynamics which should be responsible for todays tiny value of this length scale are governed by the effective potential of a Brans-Dicke type theory. Qualitative properties of this potential depend on the short distance behaviour of the unifying fundamental theory. We discuss criteria for the asymptotic behaviour of realistic cosmologies and show that the role of a possible cosmological constant is quite different from the case of standard cosmology.