Duality Rotations and BPS Monopoles with Space and Time Noncommutativity

TL;DR

This paper demonstrates SL(2,R) self-duality in noncommutative electromagnetism and DBI theory with scalar fields under light-like noncommutativity, extending duality to space-noncommutativity and analyzing monopole configurations.

Contribution

It establishes SL(2,R) self-duality in noncommutative theories with light-like noncommutativity and explores the duality's action on monopoles via the Seiberg-Witten map.

Findings

SL(2,R) self-duality holds for light-like noncommutativity.

Space-noncommutativity can be mapped to space-time noncommutativity.

Noncommutative monopoles correspond to dyonic monopoles in commutative theory.

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.