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

TL;DR

This paper explores the relationship between non-Abelian vortices and domain walls on a cylinder, revealing a duality that connects vortex moduli spaces with D-brane configurations through T-duality.

Contribution

It demonstrates a novel duality between vortex moduli spaces and D-brane configurations, linking non-Abelian vortices and domain walls via T-duality in string theory.

Findings

Identification of vortex moduli space on a cylinder.

Discovery of wall-like objects as vortices vary.

Establishment of a one-to-one correspondence with D-brane configurations.

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.