Bose-Fermi equivalence in three-dimensional noncommutative spacetime

Abstract

We study the fermionisation of Seiberg-Witten mapped action (to order θ) of the λφ4 theory coupled minimally with U(1) gauge field governed by Chern-Simons action. Starting from the corresponding partition function we derive nonperturbatively (in coupling constant) the partition function of the spin-1/2 theory following Polyakov spin factor formalism. We find that the dual interacting fermionic theory is nonlocal. This feature also persists in the limit of vanishing self-coupling. In θ → 0 limit, the commutative result is obtained. © 2008 World Scientific Publishing Company.