An Index Theorem for Domain Walls in Supersymmetric Gauge Theories

TL;DR

This paper calculates the zero modes of domain wall solutions in a supersymmetric abelian Higgs model, revealing their moduli space structure and implications for D-string configurations in string theory.

Contribution

It provides a Callias-type index calculation to determine zero modes of domain walls, connecting field theory solutions to string theory D-brane dynamics.

Findings

Most general domain wall has 2(N-1) zero modes

Zero modes correspond to positions and phases of constituent walls

Implications for D-string moduli in string theory

Abstract

The supersymmetric abelian Higgs model with N scalar fields admits multiple domain wall solutions. We perform a Callias-type index calculation to determine the number of zero modes of this soliton. We confirm that the most general domain wall has 2(N-1) zero modes, which can be interpreted as the positions and phases of (N-1) constituent domain walls. This implies the existence of moduli for a D-string interpolating between N D5-branes in IIB string theory.