Distributed Systems of Intersecting Branes at Arbitrary Angles

TL;DR

This paper develops a reduced action approach to supergravity solutions for intersecting branes at arbitrary angles, revealing a geometric structure called the H-surface and deriving new solutions for branes at SU(2) angles.

Contribution

It introduces a novel reduced Lagrangian framework encoding intersecting brane solutions and derives new configurations at arbitrary angles, expanding the understanding of supergravity solutions.

Findings

Formulation of a first order reduced Lagrangian for brane systems

Identification of the H-surface as a null geodesic embedding in configuration space

Derivation of a new solution for branes at SU(2) angles

Abstract

A `reduced' action formulation for a general class of the supergravity solutions, corresponding to the `marginally' bound `distributed' systems of various types of branes at arbitrary angles, is developed. It turns out that all the information regarding the classical features of such solutions is encoded in a first order Lagrangian (the `reduced' Lagrangian) corresponding to the desired geometry of branes. The marginal solution for a system of $N$ such distributions (for various distribution functions) span an $N$ dimensional submanifold of the fields' configuration (target) space, parametrised by a set of $N$ independent harmonic functions on the transverse space. This submanifold, which we call it as the `$H$-surface', is a null surface with respect to a metric on the configuration space, which is defined by the reduced Lagrangian. The equations of motion then transform to a set of equations describing the embedding of a null geodesic surface in this space, which is identified as the $H$-surface. Using these facts, we present a very simple derivation of the conventional orthogonal solutions together with their intersection rules. Then a new solution for a (distributed) pair of $p$-branes at SU(2) angles in $D$ dimensions is derived.