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

TL;DR

This work shows that tachyon effective actions on non-BPS D-branes and brane–antibrane systems support kink and vortex solitons whose world-volume dynamics are exactly described by Dirac-Born-Infeld actions for the corresponding lower-dimensional D-branes, with no higher-derivative corrections. The kink yields a D$(p-1)$-brane with tension ${\cal T}_{p-1} = \int_{-\infty}^{\infty} V(y)\, dy$ and localized energy, while the vortex yields a D$(p-2)$-brane with tension ${\cal T}_{p-2} = 4\pi \int_0^\infty dy \, V(y) \sqrt{ y^2 (1-\hat g(y))^2 + (\hat g'(y)/2)^2 }$; in both cases the fluctuations reduce to DBI on the soliton world-volume, with fermions and $\kappa$-symmetry realized as appropriate gauge degrees of freedom on the kink. The results reinforce the view of D-branes as tachyon solitons and reveal a close link between derivative expansions of non-BPS brane actions and their solitonic reductions, with implications for tachyon matter and couplings to gravity.

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 $κ$-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.