Aspects of brane world-volume dynamics in string theory

PhDThis thesis investigates the non-abelian dynamics of D-Brane systems in String Theory, specifically focussing on the fate of the open string Tachyon. Starting from the action of two coincident non-BPS D9-branes, we investigate kink configurations of the U(2) matrix tachyon field, considering both symmetrised (Str) and conventional (Tr) prescriptions for the trace over gauge indices of the non-BPS action. Non-abelian tachyon condensation in the theory with Tr prescription, and the resulting fluctuations about the kink profile, are shown to give rise to a theory of two coincident BPS D8-branes. Next we investigate magnetic monopole solutions of the non-abelian Dirac- Born-Infeld (DBI) action describing two coincident non-BPS D9-branes in flat space. These monopole configurations are singular in the first instance and require regularization. We discuss a suitable non-abelian ansatz which describes a pointlike magnetic monopole and show it solves the equations of motion to leading order in the regularization parameter. Fluctuations are studied and shown to describe a codimension three BPS D6-brane, a formula is derived for its tension. Finally, we investigate the dynamics of a pair of coincident D5 branes in the background of k NS5 branes. We extend Kutasov's original proposal to the nonabelian case of multiple D-Branes and find that the duality still holds provided one promotes the radial direction to a matrix valued field associated with a nonabelian geometric tachyon and a particular parametrization for the transverse scalar fields is chosen. Analytic and numerical solutions for the pair's equations of motion are found in certain simplified cases in which the U(2) symmetry is broken to U(1) U(1). For certain range of parameters these solutions describe periodic motion of the centre of mass of the pair bouncing off a finite sized throat whose minimum size is limited by the D5 branes separation