Generating branes via sigma-models

TL;DR

This paper develops solution-generating techniques for p-branes using sigma-models derived from Einstein-dilaton-antisymmetric form equations, leading to new solutions including fluxbranes, black branes, and brane intersections with internal structures.

Contribution

It introduces a sigma-model framework for generating p-brane solutions and applies various transformations to construct new and known brane configurations with internal structures.

Findings

Generated black p-branes from Schwarzschild solutions using Harrison transformation.

Constructed fluxbrane solutions and superpositions with black holes.

Provided a geometric interpretation of p-brane intersection rules.

Abstract

Starting with the D-dimensional Einstein-dilaton-antisymmetric form equations and assuming a block-diagonal form of a metric we derive a $(D-d)$-dimensional $\sigma$-model with the target space $SL(d,R)/SO(d) \times SL(2,R)/SO(2) \times R$ or its non-compact form. Various solution-generating techniques are developed and applied to construct some known and some new $p$-brane solutions. It is shown that the Harrison transformation belonging to the $SL(2,R)$ subgroup generates black $p$-branes from the seed Schwarzschild solution. A fluxbrane generalizing the Bonnor-Melvin-Gibbons-Maeda solution is constructed as well as a non-linear superposition of the fluxbrane and a spherical black hole. A new simple way to endow branes with additional internal structure such as plane waves is suggested. Applying the harmonic maps technique we generate new solutions with a non-trivial shell structure in the transverse space (`matrioshka' $p$-branes). It is shown that the $p$-brane intersection rules have a simple geometric interpretation as conditions ensuring the symmetric space property of the target space. Finally, a Bonnor-type symmetry is used to construct a new magnetic 6-brane with a dipole moment in the ten-dimensional IIA theory.