Time Dependent Solution in Open Bosonic String Field Theory

TL;DR

An exact time-dependent solution is constructed in open bosonic string field theory to model tachyon rolling on an unstable D-brane. The background is built as $\\Phi_0=\\mathcal{T}_L(\\mathcal{I})$ with a ghost-number-one operator $\\mathcal{T}$, yielding a rolling tachyon profile parameterized by the initial value $\\lambda$ and leading to a modified BRST operator $Q'$. The solution describes evolution from the unstable maximum to the tachyon vacuum as $X^0\\to\\infty$ and shows absence of perturbative open-string states in the asymptotic future, in line with Sen's conjectures. The authors discuss connections to vacuum string field theory and speculate about extensions to other branes and closed-string sectors, suggesting a framework for VSFT-like descriptions of tachyon condensation.

Abstract

In this paper we present time dependent solution of the open bosonic string field theory describing the motion of the tachyon on unstable D-brane.