Dirac-Born-Infeld action on the tachyon kink and vortex

Abstract

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