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Non-Abelian Vortices on Cylinder -- Duality between vortices and walls
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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.
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Fractional instantons in 2d $\mathbb{C}P^{N-1}$ model and 4d Yang-Mills theory with 't Hooft twists
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