Non-Abelian gapless and quasi-gapless excitations of vortices in condensed matter systems

We discuss the low energy effective theory of gapless excitations of the mass vortices of systems similar to the Ginzburg-Landau description of superfluid helium-3 in the bulk B-phase. Our approach is to determine the vortex solution by considering a specific ansatz for the order parameter and minimizing the free energy. The conditions on the β_i coefficients required for the stability of the various solutions for the order parameter are calculated. By considering the symmetries that are broken by the vortex solutions we are able to generate the modulus fields associated with the low energy excitations of the vortices. Using these fields we determine the effective free energy describing the dynamics of these excitations.