The anomaly in the central charge of the supersymmetric kink from dimensional regularization and reduction

TL;DR

This paper links the quantum anomaly in the supersymmetric kink's central charge to extra-dimensional momentum contributions, showing how dimensional regularization and reduction reveal the anomaly's origin.

Contribution

It demonstrates that the anomaly in the central charge arises from extra momentum terms in a higher-dimensional framework, connecting regularization methods to physical anomalies.

Findings

Anomaly linked to extra momentum in 2+1 dimensions

Dimensional reduction preserves supersymmetry and reveals the anomaly

Evanescent counterterms explain the anomaly in dimensional regularization

Abstract

We show that the anomalous contribution to the central charge of the 1+1-dimensional N=1 supersymmetric kink that is required for BPS saturation at the quantum level can be linked to an analogous term in the extra momentum operator of a 2+1-dimensional kink domain wall with spontaneous parity violation and chiral domain wall fermions. In the quantization of the domain wall, BPS saturation is preserved by nonvanishing quantum corrections to the momentum density in the extra space dimension. Dimensional reduction from 2+1 to 1+1 dimensions preserves the unbroken N=1/2 supersymmetry and turns these parity-violating contributions into the anomaly of the central charge of the supersymmetric kink. On the other hand, standard dimensional regularization by dimensional reduction from 1 to (1-epsilon) spatial dimensions, which also preserves supersymmetry, obtains the anomaly from an evanescent counterterm.