Static Interactions of U(N) non-Abelian Vortices

Recently, a new type of BPS vortex was found in U(N) gauge theories. This is called non-Abelian vortex and carries the non-Abelian charge CP = SU(N)C+F SU(N−1)C+F×U(1)C+F . Readers can find good reviews in and references of related works therein. In this talk we are interested in studying interactions between non-Abelian vortices which are non-BPS. The nonBPS vortices are more natural than BPS ones in a sense that the BPS always requires a fine tuning or supersymmetry. It is well known that ANO vortices in the type I system feel an attractive force while those in the type II model feel a repulsive force. Specifically we are interested in the interactions between vortices with different internal orientations, which is the distinct feature from the ANO case. This talk is based on in collaboration with R.Auzzi and W.Vince.