Noncommutative Maxwell-Chern-Simons theory in three dimensions and its dual

Abstract

We consider the Maxwell-Chern-Simons theory in noncommutative three dimensional space-time. We show that the Seiberg-Witten map is ambiguous due to the dimensional coupling constant. To get the dual theory we start from a master action obtained by promoting the global shift invariance to a local one. We also obtain the mapping between the observables of the two equivalent theories. We show that the equivalence between the Maxwell-Chern-Simons theory and the self-dual model in commutative space-time does not survive in the non-commutative setting.

14 pages, typos corrected

References in corpus (35)

• String Theory and Noncommutative Geometry
• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Noncommutative Perturbative Dynamics
• The Fermion Doubling Problem and Noncommutative Geometry
• Exact Seiberg-Witten Map, Induced Gravity and Topological Invariants in Noncommutative Field Theories
• A Consistent Noncommutative Field Theory: the Wess-Zumino Model
• Matrix ${\varphi }^4$ Models on the Fuzzy Sphere and their Continuum Limits
• Duality and Non-Commutative Gauge Theory
• Chern-Simons action in noncommutative space
• Dual equivalence between Self-Dual and Maxwell-Chern-Simons models coupled to dynamical U(1) charged matter
• Comments on Gauge Equivalence in Noncommutative Geometry
• Bosonization of Three Dimensional Non-Abelian Fermion Field Theories
• On the equivalence of the self-dual and Maxwell-Chern-Simons models coupled to Fermions
• On the Equivalence of the Maxwell-Chern-Simons Theory and a Self-Dual Model
• Towards a consistent noncommutative supersymmetric Yang-Mills theory: superfield covariant analysis
• The Noncommutative Supersymmetric Nonlinear Sigma Model
• Quantisation of θ-expanded non-commutative QED
• The Three-Dimensional Noncommutative Nonlinear Sigma Model in Superspace
• Superfield covariant analysis of the divergence structure of noncommutative supersymmetric QED${}_4$
• Hamiltonian Embedding of Self-Dual Model and Equivalence with Maxwell-Chern-Simons Theory
• Duality and Massive Gauge Invariant Theories
• Bosonization in the Noncommutative Plane
• Noncommutative Maxwell-Chern-Simons theory, duality and a new noncommutative Chern-Simons theory in d=3
• Supersymmetric Quantum Mechanics on Non-Commutative Plane
• Gauge Invariance and Duality in the Noncommutative Plane
• Duality in Noncommutative Topologically Massive Gauge Field Theory Revisited
• Supersymmetric quantum mechanics on noncommutative space
• Issues of duality on non-commutative manifolds: the {\it non-equivalence} between self-dual and topologically massive models
• Parent Action Approach for the Duality between Non-Abelian Self-Dual and Yang-Mills-Chern-Simons Models
• On duality of the noncommutative extension of the Maxwell-Chern-Simons model
• Comments on the renormalizability of the Broken Phase in Noncommutative Scalar Field Theory
• Non-commutative Duality: High Spin Fields and $C{P}^1$ Model with Hopf Term
• Nonequivalent Seiberg-Witten maps for noncommutative massive U(N) gauge theory
• Supersymmetry and Gravity in Noncommutative Field Theories

Cited by in corpus (15)

• Topics in Noncommutative Geometry Inspired Physics
• Ghost free dual vector theories in 2+1 dimensions
• On the duality of three-dimensional superfield theories
• Noncommutative Maxwell-Chern-Simons theory (I): One-loop dispersion relation analysis
• On duality of the noncommutative Maxwell-Chern-Simons theory
• A Review of Noncommutative Field Theories
• Equivalence between supersymmetric self-dual and Maxwell-Chern-Simons models coupled to a matter spinor superfield
• Dual equivalence between self-dual and topologically massive $B\wedge F$ models coupled to matter in $3+1$ dimensions
• Issues on 3D Noncommutative Electromagnetic Duality
• Aspects of Noncommutative Scalar/Tensor Duality
• On The Complete Seiberg-Witten Map For Theories With Topological Terms
• Dualization between supersymmetric self-dual and topologically massive models coupled to matter in four-dimensional superspace
• 3D and 4D noncommutative electromagnetic duality and the role of the slowly varying fields limit
• Bose-Fermi Equivalence in Three Dimensional Non-commutative Space-Time
• Electromagnetic Dualities on Noncommutative Space-Time and Symplectic Formalisms