D0 Matrix Mechanics: Topological Dynamics of Fuzzy Spaces

Abstract

We consider the physics of a matrix model describing D0-brane dynamics in the presence of an RR flux background. Non-commuting spaces arise as generic soltions to this matrix model, among which fuzzy spheres have been studied extensively as static solutions at finite N. The existence of topologicaly distinct static configurations suggests the possibility of D-brane topology change within this model, however a dynamical solution interpolating between topologies is still somewhat elusive. In this paper, we study this model in the limit of infinite dimensional matrices, where new solutions-- the fuzzy cylinder and the fuzzy plane among them-- appear. We argue that any dynamics which involves topology change will likely only occur in this limit, after which we study the decay of a fuzzy cylinder into an infinite collection of fuzzy spheres as both a classical and a quantum phenomenon. We conclude from this excercise that in certain limits, matrix models offer a viable framework in which to study topological dynamics, and could perhaps be a precursor to a viable theory of space-time topological dynamics.