Dynamics of the Dirac-Born-Infeld spike soliton - art. no. 024034

We compare oscillations of a fundamental string ending on a D3-brane in two different settings: (1) a test string radially threading the horizon of an extremal black D3-brane and (2) the spike soliton of the DBI effective act ion for a D3-brane. Previous work has shown that overall transverse modes o f the test string appear as l=0 modes of the transverse scalar fields of th e DBI system. We identify DBI world-volume degrees of freedom that have dyn amics matching those of the test-string relative transverse modes. We show that there is a map, resembling T duality, between relative and overall tra nsverse modes for the test string that interchanges Neumann and Dirichlet b oundary conditions and implies equality of the absorption coefficients for both modes. We give general solutions to the overall and relative transvers e parts of the DBI coupled gauge and scalar system and calculate absorption coefficients for the higher angular momentum modes in the low frequency li mit. We find that then is a nonzero amplitude for l>0 modes to travel out t o infinity along the spike, demonstrating that the spike remains effectivel y 3+1 dimensional.