Non-perturbative SQED beta function using functional renormalization group approach and the NSVZ exact beta function

The renormalization group equations of massive $\mathcal{N}=1$ supersymmetric quantum electrodynamics (SQED) are studied, using the functional renormalization group approach. Applying a supercovariant derivative expansion of the fields, we compute the non-perturbative beta function. In the local potential approximation, we verify the exact NSVZ $\beta$ function for the non-massive SQED limit, and we find a NSVZ relation for an effective fine-structure constant when the superpotential is considered. Furthermore, we improve the calculation of the beta function by incorporating the influence of momentum modes on the propagation of the chiral and vector superfields in the non-perturbative running of the electric charge, applying a second-order truncation for the derivative expansion, which we use to find the momentum contributions to the $\beta$ function. Again, we find a NSVZ relation for an effective fine-structure constant.Comment: 29 page

Localization of fermions in different domain wall models

Localization of fermions is studied in different gravitational domain wall models. These are generalizations of the brane-world models considered by Randall and Sundrum, but which also allow gravitational localization. Therefore, they might be considered as possible realistic scenarios for phenomenology.Comment: RevTeX, 6 pages, 10 figure

Properties of noncommutative axionic electrodynamics

Using the gauge-invariant but path-dependent variables formalism, we compute the static quantum potential for noncommutative axionic electrodynamics, and find a radically different result than the corresponding commutative case. We explicitly show that the static potential profile is analogous to that encountered in both non-Abelian axionic electrodynamics and in Yang-Mills theory with spontaneous symmetry breaking of scale symmetry.Comment: 4 pages. To appear in PR