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The Moduli Space of BPS Domain Walls

David Tong

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.

The Moduli Space of BPS Domain Walls

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.

Paper Structure

This paper contains 6 sections, 35 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Gauge Theory Domain Walls
  3. The Moduli Space of Domain Walls
  4. Fractional Vortices
  5. Acknowledgements

Figures (2)

  • Figure 1: Semi-local vortices from IIB branes. Figure 1a) has $\tilde{q}_i=0$, and finite mass BPS states exist. In Figure 1b, $\tilde{q}_i\neq 0$ and BPS states do not exist. The middle D-string has opposite orientation to the others, and breaks supersymmetry.
  • Figure 2: Kinks as fractional vortices: the $N=2$, $k=1$ model. The infinite array of branes is periodic mod 2. The 4 collective coordinates of the vortex are seen as the positions and phases of two kinks.