Dirac-Born-Infeld Action on the Tachyon Kink and Vortex

TL;DR

This paper demonstrates that the effective world-volume actions of tachyon kinks and vortices on non-BPS D-branes are exactly of the Dirac-Born-Infeld form without higher derivative corrections, confirming their BPS D-brane nature.

Contribution

It shows that the world-volume theory of tachyon kinks and vortices is precisely the DBI action, with no higher derivative corrections, extending the understanding of non-BPS D-brane dynamics.

Findings

The world-volume action on the kink is exactly the DBI action.

The vortex solution also has a DBI world-volume action.

Absence of higher derivative corrections implies a direct relation to the original effective action.

Abstract

The tachyon effective field theory describing the dynamics of a non-BPS D-brane in superstring theory has an infinitely thin but finite tension kink solution describing a codimension one BPS D-brane. We study the world-volume theory of massless modes on the kink, and show that the world volume action has precisely the Dirac-Born-Infeld (DBI) form without any higher derivative corrections. We generalize this to a vortex solution in the effective field theory on a brane-antibrane pair. As in the case of the kink, the vortex is infinitely thin, has finite energy density, and the world-volume action on the vortex is again given exactly by the DBI action on a BPS D-brane. We also discuss the coupling of fermions and restoration of supersymmetry and $\kappa$-symmetry on the world-volume of the kink. Absence of higher derivative corrections to the DBI action on the soliton implies that all such corrections are related to higher derivative corrections to the original effective action on the world-volume of a non-BPS D-brane or brane-antibrane pair.