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

Abstract

We study the Fermionisation of Seiberg-Witten mapped action (to order $θ$) of the $λϕ^{4}$ 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 $θ\to 0$ limit, the commutative result is regained.

10 pages, reoraganised the paper, removed one section