Abstract:
The recent calculation of the four-loop beta function in QCD provides further evidence that the Banks-Zaks expansion in 16half-n_f is sufficiently well behaved to be useful even for n_f=2 light flavours. This expansion inherently predicts "freezing" of the QCD couplant at low energies as a perturbative effect. We consider the e+e- and Bjorken-sum-rule cases as examples.

Abstract:
We analyse the critical exponents relating to the quark mass anomalous dimension and beta-function at the Banks-Zaks fixed point in Quantum Chromodynamics (QCD) in a variety of representations for the quark in the momentum subtraction (MOM) schemes of Celmaster and Gonsalves. For a specific range of values of the number of quark flavours, estimates of the exponents appear to be scheme independent. Using the recent five loop modified minimal subtraction (MSbar) scheme quark mass anomalous dimension and estimates of the fixed point location we estimate the associated exponent as 0.263-0.268 for the SU(3) colour group and 12 flavours when the quarks are in the fundamental representation.

Abstract:
Gauge-Yukawa Unification (GYU) is a renormalization group invariant functional relation among gauge and Yukawa couplings which holds beyond the unification point in Grand Unified Theories (GUTs). We present here various models where GYU is obtained by requiring the principles of finiteness and reduction of couplings. We examine the consequences of these requirements for the low energy parameters, especially for the top quark mass. The predictions are such that they clearly distinguish already GYU from ordinary GUTs. It is expected that it will be possible to discriminate among the various GYUs when more accurate measurements of the top quark mass are available.

Abstract:
Gauge-Yukawa unified theories, and in particular those which are finite beyond the unification scale, have been extended to include a soft supersymmetry breaking (SSB) sector. In the case of the Finite Unified Theories a new solution to the condition of two-loop finiteness of the SSB parameters is found, which requires a sum rule for the relevant scalar masses. The sum rule permits violations of the universality of the scalar masses which is found to lead to phenomenological problems. The minimal supersymmetric SU(5) Gauge-Yukawa model and two Finite-Gauge-Yukawa models have been examined using the sum rule. The characteristic features of these models are: a) the old agreement of the top quark mass prediction persists using the new data, b) the lightest Higgs boson is predicted to be around 120 GeV, c) the s-spectrum starts above 200 GeV.

Abstract:
Beyond-constant-mass approximation solutions for magnetically catalyzed fermion and scalar masses are found in a gauge Higgs-Yukawa theory in the presence of a constant magnetic field. The obtained fermion masses are several orders of magnitude larger than those found in the absence of Yukawa interactions. The masses obtained within the beyond-constant-mass approximation exactly reduce to the results within the constant-mass approach when the condition $\nu \ln (\frac{1}{\hat{m}^{2}})\ll 1$ is satisfied. Possible applications to early universe physics and condensed matter are discussed.

Abstract:
We discuss the basic idea of the Gauge-Yukawa Unification that is based on the principle of the reduction of couplings. This method of unification relies on the search of successful renormalization group invariant relations among couplings, which do not originate from symmetry principles. The predictive power of Grand Unified Theories can be increased by this method, predicting for instance values of the top quark mass consistent with the recent experimental data. The hope is that this unification attempt might shed further light on the origin of the Yukawa sector of the standard model.

Abstract:
We report on the recent progress in computing the effective supergravity action from superstring scattering amplitudes beyond the tree approximation. We discuss the moduli-dependent string loop corrections to gauge, gravitational and Yukawa couplings.

Abstract:
The possibility of radiatively generated fermion masses arising from chiral flavor violation in soft supersymmetry-breaking terms is explored. Vacuum stability constraints are considered in various classes of models, and allow in principle all of the first- and second-generation quarks and leptons and the $b$-quark to obtain masses radiatively. Radiatively induced Higgs-fermion couplings have non-trivial momentum-dependent form factors, which at low momentum are enhanced with respect to the case of tree-level Yukawa couplings. These form factors may be probed by various sum rules and relations among Higgs boson decay widths and branching ratios to fermion final states. An apparent, large, hard violation of supersymmetry also results for Higgsino couplings. Mixing between left- and right-handed scalar superpartners is enhanced. A radiative muon mass is shown to lead to a relatively large and potentially measurable contribution to the muon anomalous magnetic moment. If the light-quark masses arise radiatively, the neutron electric dipole moment is suppressed by a natural phase alignment between the masses and dipole moment, and is below the current experimental bound. The possibility of neutrino masses arising from softly broken lepton number, and concomitant enhanced sneutrino-antisneutrino oscillations, is briefly discussed.

Abstract:
Gauge-Yukawa Unification (GYU) is obtained in GUTs by searching for renormalization group invariant relations among gauge and Yukawa couplings beyond the unification scale. Of particular interest are two supersymmetric GUTs, the finite and the minimal SU(5) models. Both models provided us,among others,with predictions of the top quark mass which so far have passed successfully the tests of progressively more accurate measurements.

Abstract:
The construction of CP-invariant lattice chiral gauge theories and the construction of lattice Majorana fermions with chiral Yukawa couplings is subject to topological obstructions. In the present work we suggest lattice extensions of charge and parity transformation for Weyl fermions. This enables us to construct lattice chiral gauge theories that are CP invariant. For the construction of Majorana-Yukawa couplings, we discuss two models with symplectic Majorana fermions: a model with two symplectic doublets, and one with an auxiliary doublet.