BPS Equations and the Stress Tensor

TL;DR

This paper explores how BPS equations relate to the vanishing of stress tensor components in supersymmetric theories, highlighting the link between supersymmetry and non-interacting solitons like kinks, vortices, and dyons.

Contribution

It demonstrates the connection between supercharges, BPS states, and the stress tensor components across various supersymmetric solitonic solutions.

Findings

Stress tensor components vanish for BPS solitons

Supercharges annihilate BPS states

Connection between supersymmetry and non-interacting solitons

Abstract

We exploit the relationship between the space components of the energy-momentum tensor and the supercurrent to discuss the connection between the BPS equations and the vanishing of the components of the stress tensor in various supersymmetric theories with solitons. Using the fact that certain combination of supercharges annihilate BPS states, we show that $T_{ij}=0$ for kinks, vortices and dyons, displaying the connection between supersymmetry and non-interacting BPS solitons.