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

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) x G')/Z(n0) with G' being an arbitrary semi-simple group and no the greatest common divisor of the abelian charges of the G' invariants. The calculation is carried out using a Callias-type 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.