S Duality and Dyonic p-Brane Solutions in Type II String Theory

TL;DR

The paper addresses constructing dyonic $p$-brane solutions in string theory by exploiting duality symmetries. It develops a non-self-dual formulation of $D=10$ Type IIB supergravity and reveals two commuting $SL(2,\mathbb{R})$ structures in six dimensions—$SL(2,\mathbb{R})_{\rm IIB}$ and $SL(2,\mathbb{R})_{\rm EM}$—that act on scalars and form fields to generate dyonic configurations. Using these dualities, the authors build a ten-dimensional dyonic five-brane $5_{(10)\rm d}$ from the magnetically charged $5_{(10)\rm m}$ solution, obtaining explicit expressions for the metric, dilaton/axion, RR fields, and higher-form charges, with the brane interpolating between purely magnetic and purely electric limits and preserving $1/2$ of the supersymmetry. This work provides a concrete duality-based framework for constructing dyonic $p$-branes in Type II theories, highlighting the essential role of RR sectors and suggesting extensions to broader brane configurations and higher-dimensional theories.

Abstract

We show how a solitonic ``magnetically'' charged $p$-brane solution of a given supergravity theory, with the magnetic charge carried by an antisymmetric tensor gauge field, can be generalized to a dyonic solution. We discuss the cases of ten-dimensional and eleven-dimensional supergravity in more detail and a new dyonic five-brane solution in ten dimensions is given. Unlike the purely electrically or magnetically charged five-brane solution the dyonic five-brane contains non-zero Ramond--Ramond fields and is therefore an intrinsically type~II solution. The solution preserves half of the type~II spacetime supersymmetries. It is obtained by applying a solution-generating $SL(2,\R) \times SL(2,\R)$ $S$~duality transformation to the purely magnetically charged five-brane solution. One of the $SL(2,\R)$ duality transformations is basically an extension to the type~II case of the six-dimensional $\Z_2$ string/string duality. We also present an action underlying the type IIB supergravity theory.