Moduli space of non-abelian vortices.

We completely determine the moduli space M(N,k) of k vortices in U(N) gauge theory with N Higgs fields in the fundamental representation. Its open subset for separated vortices is found as the symmetric product (CxCP(N-1))k/(see text)k. Orbifold singularities of this space correspond to coincident vortices and are resolved resulting in a smooth moduli manifold.

Construction of non-Abelian walls and their complete moduli space.

We present a systematic method to construct exactly all Bogomol'nyi-Prasad-Sommerfield multiwall solutions in supersymmetric U(N(C)) gauge theories in five dimensions with N(F) hypermultiplets in the fundamental representation for infinite gauge coupling. The moduli space of these non-Abelian walls is found to be the complex Grassmann manifold SU(N(F)) divided by SU(N(C))xSU(N(F)-N(C))xU(1) endowed with a deformed metric.