Anti-symmetric rank-2 Matter Field on Superspace for N_(T)=2

In this work, we discuss the interaction between anti-symmetric rank-two tensor matter and topological Yang-Mills fields. The matter field considered here is the rank-2 Avdeev-Chizhov tensor matter field in a suitably extended $N_{T}=2$ SUSY. We start off from the $N_{T}=2$, D=4 superspace formulation and we go over to Riemannian manifolds. The matter field is coupled to the topological Yang-Mills field. We show that both actions are obtained as $Q-$exact forms, which allows us to write the energy-momentum tensor as $Q-$exact observables.