Quantum aspects of Seiberg-Witten map in noncommutative Chern-Simons theory

Abstract

Noncommutative Chern-Simons theory can be classically mapped to commutative Chern-Simons theory by the Seiberg-Witten map. We provide evidence that the equivalence persists at the quantum level by computing two and three-point functions of field strengths on the commutative side and their Seiberg-Witten transforms on the noncommutative side to the first nontrivial order in perturbation theory.

arXiv comment28 pages, 8 figures, 15 eps files, LaTeX2e; v2: a comment and references added in the discussion

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Cited by in corpus (12)

• Dual families of non-commutative quantum systems
• Exact Seiberg-Witten Map, Induced Gravity and Topological Invariants in Noncommutative Field Theories
• Maps for currents and anomalies in noncommutative gauge theories
• Consistent Interactions of the 2+1 Dimensional Noncommutative Chern-Simons Field
• Lowest Landau level theory of the bosonic Jain states
• Maxwell-Chern-Simons Theory is Free for Marginally Noncommutative Spacetimes
• Noncommutative N=1 super Yang-Mills, the Seiberg-Witten map and UV divergences
• Non-commutative Duality: High Spin Fields and $C{P}^1$ Model with Hopf Term
• On the quantum equivalence of commutative and noncommutative Chern-Simons theories at higher orders
• Källén-Lehmann representation of noncommutative quantum electrodynamics
• The Background Field Method and the Linearization Problem for Poisson Manifolds
• Aspects of noncommutativity in field theory, strings and membranes