Nonspherical Giant Gravitons and Matrix Theory

TL;DR

This paper explores the algebraic structure of nonspherical giant gravitons in the plane wave limit, extending the fuzzy sphere concept to fuzzy tori within matrix theory.

Contribution

It introduces a nonlinear algebra for nonspherical giant gravitons and demonstrates its role in satisfying supersymmetry conditions in matrix models.

Findings

Derived the Poisson brackets for nonspherical giant gravitons

Identified a nonlinear algebra generalizing the fuzzy sphere

Constructed finite-dimensional fuzzy torus representations

Abstract

We consider the plane wave limit of the nonspherical giant gravitons. We compute the Poisson brackets of the coordinate functions and find a nonlinear algebra. We show that this algebra solves the supersymmetry conditions of the matrix model. This is the generalization of the algebraic realization of the spherical membrane as the ``fuzzy sphere''. We describe finite dimensional representations of the algebra corresponding to the fuzzy torus.