Closed Superstring in Noncommutative Compact Spacetime

In this paper we study the effects of noncommutativity on a closed superstring propagating in the spacetime that is compactified on tori. The effects of compactification and noncommutativity appear in the momentum, quantization, supercurrent, super-conformal generators and in the boundary state of the closed superstring emitted from a D$_p$-brane with the NS$\otimes$NS background $B$-field.