String Fluid from Unstable D-branes

TL;DR

The paper analyzes Sen's unstable D-brane action to track tachyon condensation, showing that in the true vacuum the theory remains well-defined and reduces to a massive relativistic string-fluid of freely moving electric flux lines, with energy density equal to the flux density in the local co-moving frame. A finite dual Lagrangian exists, related to Nielsen-Olesen dual strings, but requires a constraint ${\cal K}\wedge{\cal K}=0$ to reproduce the original dynamics; the flux lines organize into a foliation of the worldvolume and behave as a continuum of strings (string dust) with tension $\tau=|\pi|$ in the comoving frame. The authors discuss the endpoint of tachyon condensation as a closed-string vacuum in the full theory, while the classical truncation to open-string degrees of freedom naturally yields the flux-fluid picture, and they speculate about dual mechanisms that could confine flux into unit strings and about extensions to M-theory branes. Overall, the work connects open-string effective actions to a macroscopic, relativistic string-fluid description and explores dual formulations that illuminate the fate of fundamental string charge in the true vacuum.

Abstract

We consider Sen's effective action for unstable D-branes, and study its classical dynamics exactly. In the true vacuum, the Hamiltonian dynamics remains well-defined despite a vanishing action, and is that of massive relativistic string fluid of freely moving electric flux lines. The energy(tension) density equals the flux density in the local co-moving frame. Furthermore, a finite dual Lagrangian exists and is related to the Nielsen-Olesen field theory of ``dual'' strings, supplemented by a crucial constraint. We conclude with discussion on the endpoint of tachyon condensation.