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Multi-Domain Walls in Massive Supersymmetric Sigma-Models

Jerome P. Gauntlett, David Tong, Paul K. Townsend

TL;DR

This work analyzes multi-domain-wall solutions in massive, maximally supersymmetric sigma models, showing that BPS kinks preserve half the supersymmetry and form a rich moduli space with a natural Kähler metric. Focusing on the Calabi metric on $T^ obreakerStar({ m CP}^n)$, the authors demonstrate the existence of $n$-kink configurations at arbitrary separations and identify the corresponding moduli space as toric Kähler, with each kink decomposable into $|I-J|$ fundamental kinks between adjacent vacua. The low-energy dynamics on the kink moduli space yields $1/4$-BPS charged and intersecting domain walls (Q-kinks), described by a massive sigma-model potential tied to holomorphic Killing vectors; explicit kink masses $E_{IJ}=m| u_I- u_J|$ and charges appear in this framework. The results reveal a close analogy to monopole dynamics and hint at string-theoretic applications, such as D1-D5 systems in backgrounds with $B$-fields, where kink moduli capture the relative motion of brane configurations.

Abstract

Massive maximally-supersymmetric sigma models are shown to exhibit multiple static kink-domain wall solutions that preserve 1/2 of the supersymmetry. The kink moduli space admits a natural Kahler metric. We examine in some detail the case when the target of the sigma model is given by the co-tangent bundle of CP^n equipped with the Calabi metric, and we show that there exist BPS solutions corresponding to n kinks at arbitrary separation. We also describe how 1/4-BPS charged and intersecting domain walls are described in the low-energy dynamics on the kink moduli space. We comment on the similarity of these results to monopole dynamics.

Multi-Domain Walls in Massive Supersymmetric Sigma-Models

TL;DR

This work analyzes multi-domain-wall solutions in massive, maximally supersymmetric sigma models, showing that BPS kinks preserve half the supersymmetry and form a rich moduli space with a natural Kähler metric. Focusing on the Calabi metric on , the authors demonstrate the existence of -kink configurations at arbitrary separations and identify the corresponding moduli space as toric Kähler, with each kink decomposable into fundamental kinks between adjacent vacua. The low-energy dynamics on the kink moduli space yields -BPS charged and intersecting domain walls (Q-kinks), described by a massive sigma-model potential tied to holomorphic Killing vectors; explicit kink masses and charges appear in this framework. The results reveal a close analogy to monopole dynamics and hint at string-theoretic applications, such as D1-D5 systems in backgrounds with -fields, where kink moduli capture the relative motion of brane configurations.

Abstract

Massive maximally-supersymmetric sigma models are shown to exhibit multiple static kink-domain wall solutions that preserve 1/2 of the supersymmetry. The kink moduli space admits a natural Kahler metric. We examine in some detail the case when the target of the sigma model is given by the co-tangent bundle of CP^n equipped with the Calabi metric, and we show that there exist BPS solutions corresponding to n kinks at arbitrary separation. We also describe how 1/4-BPS charged and intersecting domain walls are described in the low-energy dynamics on the kink moduli space. We comment on the similarity of these results to monopole dynamics.

Paper Structure

This paper contains 5 sections, 48 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Domain Walls and Morse Flows
  3. Domain Walls in $T^\star({\hbox{C}\hbox{P}}^n)$
  4. Dynamics of Domain Walls in $T^\star({\hbox{C}\hbox{P}}^n)$
  5. Discussion

Figures (3)

  • Figure 1: The BPS flows in the ${\hbox{C}\hbox{P}}^2$ massive sigma-model. There exists a one-parameter family of kink trajectories corresponding to the separation of two kinks. The two trajectories $3\rightarrow 2$ and $2\rightarrow 1$ may be thought of as the limit of infinitely separated kinks. The straight-line trajectory $3\rightarrow 1$ corresponds to the two kinks with zero separation.
  • Figure 2: The BPS flows in the ${\hbox{C}\hbox{P}}^3$ massive sigma-model. There now exists a two-parameter family of kink trajectories corresponding to the separation of three kinks. The flows on the faces are copies of figure 1. A typical trajectory lying within the tetrahedron is drawn.
  • Figure 3: Twice as kinky: the $D1-D5$ system in background NS $B$-field. The single D-string has a modulus in which the two kinks move apart as shown by the arrows.