Duality rotations and BPS monopoles with space and time noncommutativity

We show that noncommutative electromagnetism and Dirac-Born-Infeld (DBI) th eory with scalar fields are SL(2, R) self-dual when noncommutativity is lig ht-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 zer o 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 m ap we study the nontrivial action of this symmetry on commutative DBI theor y. In particular space-time noncommutative BPS magnetic monopoles correspon ds to commutative BPS type magnetic monopoles with both electric and magnet ic B-field background. Energy, charge and tension of these configurations a re computed and found in agreement with that of a D1-string D3-brane system . We discuss the dual string-brane configuration. (C) 2001 Elsevier Science B.V. All rights reserved.