String Fluid, Tachyon Matter, and Domain Walls

TL;DR

This paper analyzes the classical dynamics of open string tachyons coupled to gauge fields, revealing fluid-like behaviors, stability conditions, and interactions with domain walls, including the formation of BPS states during tachyon condensation.

Contribution

It provides a comprehensive Hamiltonian framework for tachyon and flux dynamics, explores solutions representing flux distributions, and investigates domain wall interactions with string fluids.

Findings

Existence of fluid-like solutions for tachyon matter and flux lines.

Stability of certain classical solutions under perturbations.

Interaction dynamics leading to fundamental string absorption and BPS configurations.

Abstract

We study classical dynamics of an open string tachyon $T$ of unstable D$p$-brane coupled to the gauge field $A_\mu$. In the vacuum with vanishing potential, V=0, two fluid-like degrees of freedom, string fluid and tachyon matter, survive the tachyon condensation. We offer general analysis of the associated Hamiltonian dynamics in arbitrary background. The canonical field equations are organized into two sets, fluid equations of motion augmented by an integrability condition. We show that a large class of motionless and degenerate family of classical solutions exist and represent arbitrary transverse distribution of tachyon matter and flux lines. We further test their stability by perturbing the fluid equation up to the second order. Second half of this note considers possibility of $V \neq 0$ in the dynamics. We incorporate $V$ in the Hamiltonian equation of motion and consider interaction between domain walls and string fluid. During initial phase of tachyon condensation, topological defect at T=0 is shown to attract nearby and parallel flux lines. The final state is fundamental strings absorbed and spread in some singular D$(p-1)$ brane soliton. When string fluid is transverse to the domain wall, the latter is known to turn into a smooth solution. We point out that a minimal solution of this sort exists and saturates a BPS energy bound of fundamental string ending on a D$(p-1)$ brane.