Duality Rotations and BPS Monopoles with Space and Time Noncommutativity

Abstract

We show that noncommutative electromagnetism and Dirac-Born-Infeld (DBI) theory with scalar fields are SL(2,R) self-dual when noncommutativity is light-like and we are in the slowly varying field approximation. This follows from SL(2,R) self-duality of the commutative DBI Lagrangian and of its zero slope limit that we study in detail. We study a symmetry of noncommutative static configurations that maps space-noncommutativity into space-time (and light-like) noncommutativity. SL(2,R) duality is thus extended to space-noncommutativity. Via Seiberg-Witten map we study the nontrivial action of this symmetry on commutative DBI theory. In particular space-time noncommutative BPS magnetic monopoles corresponds to commutative BPS type magnetic monopoles with both electric and magnetic B-field background. Energy, charge and tension of these configurations are computed and found in agreement with that of a D1-string D3-brane system. We discuss the dual string-brane configuration.

LaTeX, 31 pages, 3 figures, references added

References in corpus (6)

• Nonabelian noncommutative gauge theory via noncommutative extra dimensions
• Noncommutative Vortex Solitons
• Noncommutative Solitons in Open N=2 String Theory
• Seiberg-Witten Transforms of Noncommutative Solitons
• Dirac-Born-Infeld action, Seiberg-Witten map, and Wilson Lines
• On Duality Rotations in Light-Like Noncommutative Electromagnetism

Cited by in corpus (8)

• Quantum Spacetime Phenomenology
• AdS/CFT with Flavour in Electric and Magnetic Kalb-Ramond Fields
• Exact Seiberg-Witten Map, Induced Gravity and Topological Invariants in Noncommutative Field Theories
• Hamiltonian formulation of Noncommutative D3--Brane
• Discretized Yang-Mills and Born-Infeld actions on finite group geometries
• A Note on Duality Symmetry in Nonlinear Gauge Theories
• Issues on 3D Noncommutative Electromagnetic Duality
• Light-like noncommutativity and duality from open strings/branes