The Moduli Space of BPS Domain Walls

TL;DR

This paper explores the geometry and dynamics of BPS domain walls in N=2 SQED with multiple flavors, revealing explicit metrics, wall interactions, and their relation to vortices and fractional instantons.

Contribution

It provides the explicit two-kink metric with a toric Kahler structure and links semi-local vortices to domain wall constituents in compactified theories.

Findings

Derived the explicit two-kink metric with toric Kahler structure.

Analyzed the dynamics of colliding domain walls.

Connected semi-local vortices to fractional instantons.

Abstract

N=2 SQED with several flavors admits multiple, static BPS domain wall solutions. We determine the explicit two-kink metric and examine the dynamics of colliding domain walls. The multi-kink metric has a toric Kahler structure and we reduce the Kahler potential to quadrature. In the second part of this paper, we consider semi-local vortices compactified on circle. We argue that, in the presence of a suitable Wilson line, the vortices separate into domain wall constituents. These play the role of fractional instantons in two-dimensional gauge theories and sigma-models.