Knotted self-dual strings coupled with Kalb-Ramond field

It is shown that knotted topological strings appear at the symmetric phase of Higgs field in the context of generalized Yang-Mills Chern-Simons Higgs model. The equation of motion of the knotted strings coupled with the Kalb-Ramond field is obtained. Based on the equation of motion, we found that there is a topological constrain on the coupling term between Maxwell field and the covariant derivative of Kalb-Ramond field, the topological number of this coupling is the topological number of the abelian Chern-Simons action on the knotted topological strings