Harmonic superpositions of M-branes

TL;DR

This paper constructs and analyzes supersymmetric intersecting M-brane solutions in D=11 supergravity, revealing a simple rule for their harmonic superpositions and exploring their reductions to string and black hole configurations.

Contribution

It introduces a straightforward method for building composite supersymmetric p-brane solutions with harmonic functions, enhancing understanding of M-brane intersections and their D-brane analogues.

Findings

Constructed supersymmetric intersecting M-brane solutions

Identified a simple rule for harmonic superpositions of p-branes

Connected M-brane solutions to string and black hole configurations

Abstract

We present solutions describing supersymmetric configurations of 2 or 3 orthogonally intersecting 2-branes and 5-branes of D=11 supergravity. The configurations which preserve 1/4 or 1/8 of maximal supersymmetry are 2+2, 5+5, 2+5, 2+2+2, 5+5+5, 2+2+5 and 2+5+5 (2+2 stands for orthogonal intersection of two 2-branes over a point, etc.; p-branes of the same type intersect over (p-2)-branes). There exists a simple rule which governs the construction of composite supersymmetric p-brane solutions in D=10 and 11 with a separate harmonic function assigned to each constituent 1/2-supersymmetric p-brane. The resulting picture of intersecting p-brane solutions complements their D-brane interpretation in D=10 and seems to support possible existence of a D=11 analogue of D-brane description. The D=11 solution describing intersecting 2-brane and 5-brane reduces in D=10 to a type II string solution corresponding to a fundamental string lying within a solitonic 5-brane (which further reduces to an extremal D=5 black hole). We also discuss a particular D=11 embedding of the extremal D=4 dyonic black hole solution with finite area of horizon.