Non-Abelian Chern-Simons Vortices

We consider the bosonic sector of a N = 2 supersymmetric Chern-Simons-Higgs theory in 2 + 1 dimensions. The gauge group is U(1) × SU(N) and has Nf flavors of fundamental matter fields. The model supports non-Abelian (axially symmetric) vortices when Nf ≥ N , which have internal (orientational) moduli. When Nf > N , the solutions acquire additional collective coordinates parameterizing their transverse size. We solve the BPS equations numerically and obtain local (Nf = N) and semi-local (Nf > N) string solutions. A CP N−1 low-energy effective action for the orientational moduli is obtained in both cases. In the semilocal case there is an additional term in the effective action induced by the transverse size moduli. We find such term in the limit of large transverse size, where exact solutions can be obtained analytically.