Dynamics of the DBI Spike Soliton

TL;DR

This paper compares oscillations of a fundamental string near a black D3-brane with the spike soliton in the DBI action, revealing a T-duality-like map and showing spike's effective 3+1-dimensionality through absorption analysis.

Contribution

It identifies a T-duality-like correspondence between modes in the DBI spike and test-string oscillations, and calculates absorption coefficients for higher angular momentum modes.

Findings

Matching dynamics of transverse modes between test-string and DBI spike.

Existence of a T-duality-like map interchanging boundary conditions.

Nonzero amplitude for l>0 modes indicates spike's effective 3+1-dimensionality.

Abstract

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 action for a D3-brane. Previous work has shown that overall transverse modes of the test-string appear as l=0 modes of the transverse scalar fields of the DBI system. We identify DBI world-volume degrees of freedom that have dynamics matching those of the test-string relative transverse modes. We show that there is a map, resembling T-duality, between relative and overall transverse modes for the test-string that interchanges Neumann and Dirichlet boundary conditions and implies equality of the absorption coefficients for both modes. We give general solutions to the overall and relative transverse parts of the DBI coupled gauge and scalar system and calculate absorption coefficients for the higher angular momentum modes in the low frequency limit. We find that there is a nonzero amplitude for l>0 modes to travel out to infinity along the spike, demonstrating that the spike remains effectively 3+1-dimensional.