Non-renormalization theorems of Supersymmetric QED in the Wess-Zumino gauge

TL;DR

This paper proves non-renormalization theorems in supersymmetric QED using algebraic renormalization, extending the gauge coupling to an external superfield, and establishes a comprehensive symmetry framework including the axial anomaly.

Contribution

It introduces a novel algebraic approach to derive non-renormalization theorems in SQED by extending gauge coupling and employing supercoupling and external multiplets.

Findings

Non-renormalization of chiral vertices confirmed.

Photon self-energy non-renormalization established.

Explicit form of the gauge beta-function derived.

Abstract

The non-renormalization theorem of chiral vertices and the generalized non-renormalization theorem of the photon self energy are derived in SQED on the basis of algebraic renormalization. For this purpose the gauge coupling is extended to an external superfield. This extension already provides detailed insight into the divergence structure. Moreover, using the local supercoupling together with an additional external vector multiplet that couples to the axial current, the model becomes complete in the sense of multiplicative renormalization, with two important implications. First, a Slavnov--Taylor identity describing supersymmetry, gauge symmetry, and axial symmetry including the axial anomaly can be established to all orders. Second, from this Slavnov-Taylor identity we can infer a Callan-Symanzik equation expressing all aspects of the non-renormalization theorems. In particular, the gauge $\beta$-function appears explicitely in the closed form.