On Time-dependent Collapsing Branes and Fuzzy Odd-dimensional Spheres
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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^3 and S^5 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 fuzzy-S^3 and S^5 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^3, fuzzy-S^5 and general fuzzy odd-spheres.
35 pages, latex; v2: discussion in Appendix B on the large-N limit of the associator is modified, main results of paper unchanged
35 pages, latex; v2: discussion in Appendix B on the large-N limit of the associator is modified, main results of paper unchanged