(p,q) 5-Branes in Non-Zero B-Field

TL;DR

This paper constructs an exact SL(2;Z)-covariant supergravity solution for (p,q) 5-branes in a non-zero B-field, elucidating the relationship between background tensor fields, Born-Infeld degrees, and non-commutativity.

Contribution

It provides the first exact non-linear supergravity solution for (p,q) 5-branes with a constant B-field, clarifying their physical degrees of freedom and background field relations.

Findings

Derived an SL(2;Z)-covariant supergravity solution.

Analyzed the metric space-times with maximal tensor values.

Connected background tensor fields to non-commutativity parameters.

Abstract

We consider type IIB (p,q) 5-branes in constant non-zero background tensor potentials, or equivalently, with finite constant field strength on the brane. 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-times are analysed, with special emphasis on the limiting cases with maximal values of the tensor. The analysis provides an answer to how the various background tensor fields are related to Born-Infeld degrees of freedom and to non-commutativity parameters.