Currents in supersymmetric field theories

TL;DR

This paper develops a formalism for constructing supercurrents in N=1 supersymmetric theories, enabling derivation of the all-order NSVZ beta function through anomaly matching.

Contribution

It introduces a general method to construct and improve supercurrents including gauge and chiral superfields, and derives the NSVZ beta function algebraically.

Findings

Constructed supercurrent structures with specific energy-momentum and R currents.

Derived the all-order NSVZ beta function via anomaly cancellation.

Provided a framework for describing gauge couplings as background or propagating fields.

Abstract

A general formalism to construct and improve supercurrents and source or anomaly superfields in two-derivative N=1 supersymmetric theories is presented. It includes arbitrary gauge and chiral superfields and a linear superfield coupled to gauge fields. These families of supercurrent structures are characterized by their energy-momentum tensors and R currents and they display a specific relation to the dilatation current of the theory. The linear superfield is introduced in order to describe the gauge coupling as a background (or propagating) field. Supersymmetry does not constrain the dependence on this gauge coupling field of gauge kinetic terms and holomorphicity restrictions are absent. Applying these results to an effective (Wilson) description of super-Yang-Mills theory, matching or cancellation of anomalies leads to an algebraic derivation of the all-order NSVZ beta function.