Duality in Noncommutative Topologically Massive Gauge Field Theory Revisited

Abstract

We introduce a master action in noncommutative space, out of which we obtain the action of the noncommutative Maxwell-Chern-Simons theory. Then, we look for the corresponding dual theory at both first and second orders in the noncommutative 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 noncommutative version, including a cubic term. Since this resulting theory is also equivalent to the noncommutative massive Thirring model in the large fermion mass limit, we remove, as a byproduct, the obstacles arising in the generalization to noncommutative space, and to the first nontrivial order in the noncommutative parameter, of the bosonization in three dimensions. Then, performing calculations at the second order in the noncommutative parameter, we explicitly compute a new dual theory which differs from the noncommutative 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 noncommutative space of bosonization in three dimensions is possible only when considering the first non-trivial corrections over ordinary space.

14 pages, Latex. v2: comments and references added, minor changes. v3: analysis extended to the second order in the noncommutative parameter, references and discussions added. v4: added discussion on higher order corrections, minor changes

References in corpus (6)

• Bosonization in the Noncommutative Plane
• Noncommutative Maxwell-Chern-Simons theory, duality and a new noncommutative Chern-Simons theory in d=3
• Gauge Invariance and Duality in the Noncommutative Plane
• Chiral Bosons in Noncommutative Spacetime
• Duality between Noncommutative Yang-Mills-Chern-Simons and Non-Abelian Self-Dual Models
• Parent Actions, Dualities and New Weyl-invariant Actions of Bosonic p-branes

Cited by in corpus (20)

• Topics in Noncommutative Geometry Inspired Physics
• Einstein-Cartan formulation of Chern-Simons Lorentz-violating Gravity
• Noncommutative Maxwell-Chern-Simons theory in three dimensions and its dual
• Ghost free dual vector theories in 2+1 dimensions
• On duality of the noncommutative extension of the Maxwell-Chern-Simons model
• On the duality of three-dimensional superfield theories
• Maxwell-Chern-Simons Theory is Free for Marginally Noncommutative Spacetimes
• Three dimensional noncommutative bosonization
• Non-commutative solitons and strong-weak duality
• On duality of the noncommutative Maxwell-Chern-Simons theory
• Higher derivative Chern-Simons extension in the noncommutative QED${}_3$
• Equivalence between supersymmetric self-dual and Maxwell-Chern-Simons models coupled to a matter spinor superfield
• Non-commutative Duality: High Spin Fields and $C{P}^1$ Model with Hopf Term
• Soldering Formalism in Noncommutative Field Theory: A Brief Note
• Quantum equivalence between the self-dual and the Maxwell-Chern-Simons models nonlinearly coupled to U(1) scalar fields
• Aspects of Noncommutative Scalar/Tensor Duality
• 3D and 4D noncommutative electromagnetic duality and the role of the slowly varying fields limit
• Higher-derivative $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetric Maxwell-Chern-Simons theories at one loop in superspace
• Electromagnetic Dualities on Noncommutative Space-Time and Symplectic Formalisms
• Bose-Fermi Equivalence in Three Dimensional Non-commutative Space-Time