Emergent Kalb-Ramond fields from a dimer model

We discuss the emergence of a Kalb-Ramond field and string charge in the lattice and consider the local bosonic model with rotor variables placed on the faces of a cubic lattice. We give the coupling model consisting of the Maxwell fields and the Kalb-Ramond field. This construction naturally incorporates the emerging coupling between both gauge and string fields. In the process, an object that resembles a D-brane on the lattice is introduced.