Effective Theory on Non-Abelian Vortices in Six Dimensions

TL;DR

This paper derives an effective field theory describing non-Abelian vortices in six-dimensional supersymmetric gauge theories, classifying their moduli and constructing the associated low-energy dynamics.

Contribution

It introduces a systematic method for deriving the most general effective Lagrangian for vortex moduli fields respecting symmetry.

Findings

Identified and classified moduli fields into Nambu-Goldstone and quasi-Nambu-Goldstone modes.

Constructed effective gauge theories on vortex world volumes.

Described the moduli space as a vector bundle over the complex Grassmann manifold.

Abstract

Non-Abelian vortices in six spacetime dimensions are obtained for a supersymmetric U(N) gauge theory with N hypermultiplets in the fundamental representation. Massless (moduli) fields are identified and classified into Nambu-Goldstone and quasi-Nambu-Goldstone fields. Effective gauge theories for the moduli fields are constructed on the four-dimensional world volume of vortices. A systematic method to obtain the most general form of the effective Lagrangian consistent with symmetry is proposed. The moduli space for the multi-vortices is found to be a vector bundle over the complex Grassmann manifold.