A nonperturbative method for the Yang–Mills Lagrangian

Using the properties of the partition function for a Yang–Mills theory we compute simple relations among the renormalization constants. In the particular case of the background gauge field method we obtain that the all orders beta function for the gauge coupling constant contains only the first two orders coefficients different than zero and thus corresponds to the 't Hooft scheme.

Parameterizing the SFC Baryogenesis Model

We have numerically explored the scalar field condensate baryogenesis model for numerous sets of model’s parameters, within their natural range of values. We have investigated the evolution of the baryon charge carrying field, the evolution of the baryon charge contained in the scalar field condensate, and the final value of the generated baryon charge on the model’s parameters: the gauge coupling constantα, the Hubble constant at the inflationary stageHI, the massm, and the self-coupling constantsλi.

GEOMETRIC ENGINEERING LIMIT AND WEAK GRAVITY CONJECTURE

We analyze the coupled [Formula: see text] supergravity and Yang-Mills system using holomorphy, near the rigid limit where the former decouples from the latter. We find that there appears generically a new mass scale around gMpl where g is the gauge coupling constant and Mpl is the Planck scale. This is in accord with the weak-gravity conjecture proposed recently.

PHENOMENOLOGICAL STRING COSMOLOGY AND ITS IMPLICATIONS

We have explored the possibility that the universe at very early stage was dominated by (macroscopic) heterotic strings. We have found that the dimensionless parameter Gμ for the heterotic strings varies from 10-2 to 10-4 as the universe evolve from the matter dominance to radiation dominance. This led to the interesting consequence of epoch dependent gauge coupling constant. The gauge coupling constant at early times was found to be much stronger than the present strong interaction.

DUALITY SYMMETRIES IN GENERALIZED COXETER ORBIFOLDS

We derive the duality symmetries relevant to moduli-dependent gauge coupling constant threshold corrections, in generalized Coxeter ZN orbifolds. The underlying sixdimensional lattice of the heterotic string theory is not assumed to decompose into a direct sum of a four-dimensional and a two-dimensional sublattice and the point group leaves fixed a two-dimensional sublattice.

COMPLETE CLASSES OF GUTS WITH VANISHING ONE-LOOP BETA FUNCTIONS

By explicit solution of the one-loop finiteness conditions for all dimensionless coupling constants (i.e. the gauge coupling constant as well as Yukawa and quartic scalar-boson self-interaction coupling constants), two classes of grand unified theories characterized by renormalization-group beta functions which all vanish at least at the one-loop level are constructed and analyzed with respect to the (suspected) appearance of quadratic divergences, with the result that without exception in all of these models the masses of both vector and scalar bosons receive quadratically divergent one-loop contributions.