The moduli space of non-Abelian vortices in Yang-Mills-Chern-Simons-Higgs theory

Abstract

We determine the dimension of the moduli space of non-Abelian vortices in Yang-Mills-Chern-Simons-Higgs theory in 2 + 1 dimensions for gauge groups G = U(1) × G with G being an arbitrary semi-simple group. The calculation is carried out using a Calliastype index theorem, the moduli matrix approach and a D-brane setup in Type IIB string theory. We prove that the index theorem gives the number of zeromodes or moduli of the non-Abelian vortices, extend the moduli matrix approach to the Yang-Mills-Chern-Simons-Higgs theory and finally derive the effective Lagrangian of Collie and Tong using string theory.