On Time-dependent Collapsing Branes and Fuzzy Odd-dimensional Spheres

We study the time-dependent dynamics of a collection of N collapsing/expanding D0-branes in type IIA String Theory. We show that the fuzzy-S and S provide time-dependent solutions to the Matrix Model of D0-branes and its DBI generalisation. Some intriguing cancellations in the calculation of the non-abelian DBI Matrix actions result in the fuzzyS and S having the same dynamics at large-N . For the Matrix model, we find analytic solutions describing the time-dependent radius, in terms of Jacobi elliptic functions. Investigation of the physical properties of these configurations shows that there are no bounces for the trajectory of the collapse at large-N . We also write down a set of useful identities for fuzzy-S, fuzzy-S and general fuzzy odd-spheres. †{c.papageorgakis, s.ramgoolam}@qmul.ac.uk