A Note on Supersymmetric WZW term in Four Dimensions

TL;DR

This paper investigates the supersymmetric WZW term in four dimensions, exploring conditions under which derivative terms on auxiliary fields can be eliminated, and presents a higher derivative term free from such issues.

Contribution

It demonstrates that all derivative terms in the supersymmetric WZW term can be canceled if the anomalous term vanishes, and provides the first example of a higher derivative term without this problem.

Findings

All derivative terms can be canceled if the anomalous term vanishes.

A new higher derivative term free from derivative issues is constructed.

Conditions for eliminating derivative terms in supersymmetric WZW are clarified.

Abstract

We reconsider the supersymmetric Wess-Zumino-Witten (SWZW) term in four dimensions. It has been known that the manifestly supersymmetric form of the SWZW term includes derivative terms on auxiliary fields, the highest components of chiral superfields, and then we cannot eliminate them by their equations of motion. We discuss a possibility for the elimination of such derivative terms by adding total derivative terms. Although the most of derivative terms can be eliminated as in this way, we find that all the derivative terms can be canceled, if and only if an anomalous term in SWZW term vanishes. As a byproduct, we find the first example of a higher derivative term free from such a problem.