Topological-charge anomalies in supersymmetric theories with domain walls

TL;DR

This paper investigates topological-charge anomalies in supersymmetric domain walls, revealing dual fermionic and bosonic contributions to the anomaly and analyzing quantum modifications of the supercharge algebra.

Contribution

It provides a detailed analysis of topological-charge anomalies in supersymmetric domain walls, highlighting the dual fermionic and bosonic nature and the role of supercurrent improvements.

Findings

Quantum modifications of the supercharge algebra include both short- and long-distance effects.

The central-charge anomaly can be transferred between fermionic and bosonic sectors via supercurrent improvement.

The one-loop superfield effective action confirms the anomaly and BPS saturation.

Abstract

Domain walls in 1+2 dimensions are studied to clarify some general features of topological-charge anomalies in supersymmetric theories, by extensive use of a superfield supercurrent. For domain walls quantum modifications of the supercharge algebra arise not only from the short-distance anomaly but also from another source of long-distance origin, induced spin in the domain-wall background, and the latter dominates in the sum. A close look into the supersymmetric trace identity, which naturally accommodates the central-charge anomaly and its superpartners, shows an interesting consequence of the improvement of the supercurrent: Via an improvement the anomaly in the central charge can be transferred from induced spin in the fermion sector to an induced potential in the boson sector. This fact reveals a dual character, both fermionic and bosonic, of the central-charge anomaly, which reflects the underlying supersymmetry. The one-loop superfield effective action is also constructed to verify the anomaly and BPS saturation of the domain-wall spectrum.