On brane solutions in M(atrix) theory

TL;DR

This paper investigates brane solutions in M(atrix) theory, demonstrating how certain geometries emerge in the large N limit and analyzing their supersymmetry properties.

Contribution

It introduces new brane solutions with specific geometries and provides a detailed group theoretic analysis of known solutions within M(atrix) theory.

Findings

World volume coordinates emerge for G=SU(N)

Smooth manifold structures appear in the large N limit

Solutions are non-supersymmetric but part of a supersymmetric set

Abstract

In this paper we consider brane solutions of the form $G/H$ in M(atrix) theory, showing the emergence of world volume coordinates for the cases where $G=SU(N)$. We examine a particular solution with a world volume geometry of the form ${\bf CP}^2 \times S^1$ in some detail and show how a smooth manifold structure emerges in the large $N$ limit. In this limit the solution becomes static; it is not supersymmetric but is part of a supersymmetric set of configurations. Supersymmetry in small locally flat regions can be obtained, but this is not globally defined. A general group theoretic analysis of the previously known spherical membrane solutions is also given.