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

TL;DR

This paper employs the functional renormalization group approach to derive a non-perturbative beta function for massive  supersymmetric QED, revealing a close relationship with the NSVZ exact beta function and analyzing the massless limit.

Contribution

It introduces a non-perturbative calculation of the SQED beta function using the functional renormalization group, connecting it to the NSVZ relation and including momentum mode effects.

Findings

The non-perturbative beta function closely matches the NSVZ form.

Inclusion of momentum modes refines the beta function calculation.

The NSVZ relation holds for an effective fine-structure constant.

Abstract

The renormalization group equations of massive $\mathcal{N}=1$ supersymmetric quantum electrodynamics (SQED) are studied using the functional renormalization group approach. A non-perturbative form of the beta function has been computed via a derivative expansion of the effective action. In the local potential approximation, the functional form of the non-perturbative beta function is closely related to the form of the NSVZ exact beta function; this relationship is exact if an effective fine-structure constant is defined. The non-massive limit of the same is also analyzed. Furthermore, the calculation of the beta function has been improved by incorporating the influence of momentum modes on the propagation of the 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 the NSVZ relation for an effective fine-structure constant.