Three dimensional noncommutative bosonization

TL;DR

This paper extends the bosonization process to 2+1-dimensional noncommutative spacetime, showing that the large mass limit yields a noncommutative Chern-Simons action and discussing the induction of NC Yang-Mills action.

Contribution

It demonstrates that bosonization in NC spacetime leads to a NC Chern-Simons action in the large mass limit, valid to all orders in the noncommutative parameter.

Findings

Large mass limit yields NC Chern-Simons action

Result valid to all orders in noncommutative parameter

Induction of NC Yang-Mills action discussed

Abstract

We consider the extension of the 2+1-dimensional bosonization process in Non-Commutative (NC) spacetime. We show that the large mass limit of the effective action obtained by integrating out the fermionic fields in NC spacetime leads to the NC Chern-Simons action. The present result is valid to all orders in the noncommutative parameter $\theta$. We also discuss how the NC Yang-Mills action is induced in the next to leading order.