String fluid, tachyon matter, and domain walls

We study classical dynamics of an open string tachyon $T$ of unstableD$p$-brane coupled to the gauge field $A_\mu$. In the vacuum with vanishingpotential, V=0, two fluid-like degrees of freedom, string fluid and tachyonmatter, survive the tachyon condensation. We offer general analysis of theassociated Hamiltonian dynamics in arbitrary background. The canonical fieldequations are organized into two sets, fluid equations of motion augmented byan integrability condition. We show that a large class of motionless anddegenerate family of classical solutions exist and represent arbitrarytransverse distribution of tachyon matter and flux lines. We further test theirstability 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 considerinteraction between domain walls and string fluid. During initial phase oftachyon condensation, topological defect at T=0 is shown to attract nearby andparallel flux lines. The final state is fundamental strings absorbed and spreadin some singular D$(p-1)$ brane soliton. When string fluid is transverse to thedomain wall, the latter is known to turn into a smooth solution. We point outthat a minimal solution of this sort exists and saturates a BPS energy bound offundamental string ending on a D$(p-1)$ brane.Comment: 37 pages, 3 figure