#### Alladi Ramakrishnan Hall

#### Vortices in non-Abelian gauge theories

#### Chandrasekhar Chatterjee

##### Keio University, Japan

*In this lecture I would discuss vortices in non-Abelian gauge theory with bi-fundamental scalars. We start with U(1) X SU(N)c X SU(N)f invariant action with U(1) X SU(N) gauge fields interacting with bi-fundamental scalars. The vacuum expectation value of the scalar field keeps the diagonal SU(N) color-flavor symmetry unbroken at low energies. This generates vortex configurations containing non-Abelian fluxes due to existence of non trivial fundamental group of vacuum manifold. After performing BPS completion we write BPS equations and discuss possible numerical solutions. The unbroken SU(N) color-flavor group is broken in the presence of vortices and create degenerate solutions. This generates CP(N-1) Nambu-Goldstone zero modes inside the vortices. We would discuss the low energy effective action described by CP(N-1) sigma model. Since these vortices may be important for understanding monopole vortex complex(confinement of dual charges), we discuss briefly the possible monopole vortex complexes in non-supersymmetric cases including dense QCD CFL phase.*

Done