Tachyon condensation and universality of DBI action

TL;DR

This work demonstrates that the low-energy dynamics of massless fluctuations around a tachyonic soliton, representing a codimension-one D-brane, is governed by the Dirac-Born-Infeld (DBI) action. By starting from an open-string sigma-model–inspired effective action with tachyon T and abelian field F, it identifies a translational collective coordinate Φ as the D-brane’s transverse fluctuation and derives, via a non-linear collective-coordinate ansatz T(y1) with y1 = (x1 − Φ)/β, the DBI form S = T_{d−2} ∫ d^{d−1}x √det(δ_{ij} + F_{ij} + ∂_iΦ ∂_jΦ). The world-sheet perspective via the boundary sigma-model confirms this result: tachyon condensation deforms boundary conditions so the IR fixed point yields the DBI action for the remaining world-volume fields, with the collective coordinate coupling encoded in a generalized boundary action that reproduces the correct beta-functions and equations of motion. Overall, the paper shows the DBI action’s universality, arising from the open-string sigma-model structure rather than details of the tachyon potential, and clarifies how brane collective coordinates appear in both EFT and world-sheet formalisms.

Abstract

We show that a low-energy action for massless fluctuations around a tachyonic soliton background representing a codimension one D-brane coincides with the Dirac-Born-Infeld action. The scalar modes which describe transverse oscillations of the D-brane are translational collective coordinates of the soliton. The appearance of the DBI action is a universal feature independent of details of a tachyon effective action, provided it has the structure implied by the open string sigma model partition function.