Non-Abelian Vortices on Cylinder -- Duality between vortices and walls

TL;DR

This work demonstrates a duality between non-Abelian vortices on a cylinder and domain walls, cast through a T-duality between D-brane configurations. By employing the moduli-matrix formalism and Scherk–Schwarz reduction, the authors connect vortex moduli to kinky D-brane wall configurations and establish a one-to-one correspondence between the vortex moduli space and wall configurations. They show that periodically arranged vortices on $oldsymbol{R} imes S^1$ split into wall-like objects as moduli grow, and twisted boundary conditions yield domain walls as kinks of Wilson lines on the dual circle. The analysis yields explicit moduli-space structures for single and double vortices and suggests broader implications for dualities among solitons and their stringy realizations.

Abstract

We investigate vortices on a cylinder in supersymmetric non-Abelian gauge theory with hypermultiplets in the fundamental representation. We identify moduli space of periodic vortices and find that a pair of wall-like objects appears as the vortex moduli is varied. Usual domain walls also can be obtained from the single vortex on the cylinder by introducing a twisted boundary condition. We can understand these phenomena as a T-duality among D-brane configurations in type II superstring theories. Using this T-duality picture, we find a one-to-one correspondence between the moduli space of non-Abelian vortices and that of kinky D-brane configurations for domain walls.

Figures (17)

• Figure 1: Two separated lumps (left) approach each other (middle). A ring appears at the coincident limit (right).
• Figure 2: Energy density of two coincident semi-local vortices in the case of $N_{\rm C}=1$ and $N_{\rm F}=2$. The horizontal axis denotes the radius from the coincident point and the vertical axis denotes the energy density. Energy densities with various values of the size modulus $|a|$ are plotted. It has a huge central peak for $a=0$, whereas a central hole with a ring structure develops for larger $|a|$.
• Figure 3: Energy density of the periodically arranged vortices in the strong coupling limit $g \rightarrow \infty$.
• Figure 4: Examples: $R=1, \space m_1=0.2, \space m_2=-0.15$ (a) $a_1=e^{-0.6},a_2=1$, (b) $a_1=e^{5.5},a_2=e^{3}$
• Figure 5: Profile of small size limit of $\hat{\Sigma}(x^1)$ in the strong gauge coupling limit