Supersymmetry and Bogomol'nyi equations in the Abelian Higgs Model

TL;DR

The paper analyzes how $N=2$ supersymmetry and Bogomol'nyi equations intersect in the Abelian Higgs model, showing that requiring $\lambda = \frac{e^2}{8}$ enables an $N=2$ extension and the appearance of a central charge that matches the topological charge. From the SUSY algebra, an energy bound $E \ge \frac{2\pi}{e}|n|$ emerges, saturated by Bogomol'nyi equations which link the gauge field to the Higgs condensate. The same structure is shown to hold upon dimensional reduction to $d=2$ in Euclidean space, where self-dual equations again arise and protect the bound. Overall, the work clarifies why gauge theories with spontaneous symmetry breaking naturally couple $N=2$ SUSY to Bogomol'nyi dynamics, with implications for solitons and possibly gravity-inspired contexts.

Abstract

The N=2 supersymmetric extension of the 2+1 dimensional Abelian Higgs model is discussed. By analysing the resulting supercharge algebra, the connection between supersymmetry and Bogomol'nyi equations is clarified. Analogous results are presented when the model is considered in 2-dimensional (Euclidean) space.