3D and 4D noncommutative electromagnetic duality and the role of the slowly varying fields limit
arXiv:hep-th/0611050
Abstract
We study classical noncommutative (NC) electromagnetic duality in both 3D and 4D space-times through the Seiberg-Witten (SW) map to all orders in theta. We evaluate the role of space-time dimensions, of the gauge coupling constant g^2 inversion, of the slowly varying fields (SVF) limit and of the rule theta --> g^2 *theta (where * is the Hodge duality operator), which was originally found in the 4D space-time. Among our results, a new scalar picture for NC electromagnetism to second order in theta is established, a formula which simplifies considerably the application of the SW map in 3D is presented and we show that the SVF limit has a crucial role in this duality starting from the third order in theta for any dimension: outside this limit the symmetry between theta and g^2 *theta is lost.
arXiv comment10 pages, PoS style, Fifth International Conference on Mathematical Methods in Physics
References in corpus (14)
- Space-Time Noncommutative Field Theories And Unitarity
- Noncommutative Field Theories and Gravity
- Physical Instances of Noncommuting Coordinates
- Exact Seiberg-Witten Map, Induced Gravity and Topological Invariants in Noncommutative Field Theories
- Duality and Non-Commutative Gauge Theory
- Seiberg-Witten-type Maps for Currents and Energy-Momentum Tensors in Noncommutative Gauge Theories
- Noncommutative Electrodynamics
- Bosonization in the Noncommutative Plane
- Noncommutative Maxwell-Chern-Simons theory, duality and a new noncommutative Chern-Simons theory in d=3
- Duality in Noncommutative Topologically Massive Gauge Field Theory Revisited
- Noncommutative Maxwell-Chern-Simons theory in three dimensions and its dual
- Duality between Noncommutative Yang-Mills-Chern-Simons and Non-Abelian Self-Dual Models
- On duality of the noncommutative extension of the Maxwell-Chern-Simons model
- Issues on 3D Noncommutative Electromagnetic Duality