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

TL;DR

This paper investigates the time-dependent behavior of collapsing and expanding D0-branes in type IIA String Theory, revealing solutions involving fuzzy spheres and analyzing their dynamics and properties at large N.

Contribution

It presents new analytic solutions for fuzzy S^3 and S^5 in the Matrix Model, showing their identical large-N dynamics and providing identities for fuzzy odd-spheres.

Findings

Fuzzy S^3 and S^5 have identical large-N dynamics.

Analytic solutions for radius evolution involve Jacobi elliptic functions.

No bounce occurs in the collapse trajectory at large N.

Abstract

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.