Bose-Fermi Equivalence in Three Dimensional Non-commutative Space-Time

We study the Fermionisation of Seiberg-Witten mapped action (to order $\theta$) of the $\lambda {\varphi }^4$ theory coupled minimally with U(1) gauge field governed by Chern-Simon action. Starting from the corresponding partition function we derive non-perturbatively (in coupling constant) the partition function of the spin 1/2 theory following Polyakov spin factor formalism. We find the dual interacting fermionic theory is non local. This feature persist also in the limit of vanishing self coupling. In $\theta \to 0$ limit, the commutative result is regained.