The BV Formalization of Chern-Simons Theory on Deformed Superspace

In this paper we will study non-abelian Chern-Simons theory on a deformed superspace. We will deform the superspace in such a way that it includes the noncommutativity between bosonic and fermionic coordinates. We will first analyse the BRST and the anti-BRST symmetries of the Chern-Simons theory on this deformed superspace. Then we will analyse the extended BRST and the extended anti-BRST symmetries of this theory in the Batalin-Vilkovisky (BV) formalism. Finally, we will express these extended BRST and extended anti-BRST symmetries in extended superspace formalism by introducing new Grassmann coordinates.