Duality in noncommutative topologically massive gauge field theory revisited
High Energy Section, Abdus Salam ICTP, Strada Costiera 11, 34014, Trieste, Italy
2 Departamento de Teoria de Campos e Partículas (DCP), Centro Brasileiro de Pesquisas Físicas (CBPF), Rua Dr. Xavier Sigaud 150, 22290-180, Rio de Janeiro, RJ, Brazil
3 Instituto de Física Teórica (IFT), Universidade Estadual Paulista (UNESP), Rua Pamplona 145, 01405-900, São Paulo, SP, Brazil
* e-mail: firstname.lastname@example.org
We introduce a master action in non-commutative space, out of which we obtain the action of the non-commutative Maxwell-Chern-Simons theory. Then, we look for the corresponding dual theory at both first and second order in the non-commutative parameter. At the first order, the dual theory happens to be, precisely, the action obtained from the usual commutative self-dual model by generalizing the Chern-Simons term to its non-commutative version, including a cubic term. Since this resulting theory is also equivalent to the non-commutative massive Thirring model in the large fermion mass limit, we remove, as a byproduct, the obstacles arising in the generalization to non-commutative space, and to the first non-trivial order in the non-commutative parameter, of the bosonization in three dimensions. Then, performing calculations at the second order in the non-commutative parameter, we explicitly compute a new dual theory which differs from the non-commutative self-dual model and, further, differs also from other previous results and involves a very simple expression in terms of ordinary fields. In addition, a remarkable feature of our results is that the dual theory is local, unlike what happens in the non-Abelian, but commutative case. We also conclude that the generalization to non-commutative space of bosonization in three dimensions is possible only when considering the first non-trivial corrections over ordinary space.
© Springer-Verlag, 2004