(p, q) 5-Branes in non-zero B-field

We consider type-IIB (p, q) 5-branes in constant non-zero background tensor potentials, or equivalently, with finite constant field strength on the br ane. At linear level, zero-modes are introduced and the physical degrees of freedom are found to be parametrised by a real 2- or 4-form field strength on the brane. An exact, SL(2, Z)-covariant solution to the full non-linear supergravity equations is then constructed. The resulting metric space-tim es are analysed, with special emphasis on the limiting cases with maximal v alues of the tensor. The analysis provides an answer to how the various bac kground tensor fields are related to Born-Infeld degrees of freedom and to non-commutativity parameters.