Classical Solutions in String Field Theory Around the Tachyon Vacuum

TL;DR

The paper demonstrates that cubic open string field theory around the tachyon vacuum admits classical D-brane solutions through a universal ghost factor and a factorized matter sector. It provides closed-form matter states for D-branes of all dimensions, identifies the D25-brane with the matter part of the sliver state, and constructs lower-dimensional lump solutions whose tension ratios match known results via determinants of infinite matrices. The analysis combines oscillator-Neumann-coefficient methods with level truncation to validate the sliver identification and the lump constructions, while highlighting gauge-related ambiguities and remaining open questions about the ghost sector and fluctuations. Overall, the work offers a concrete, largely analytic framework to realize D-branes in a tachyon-vacuum string field theory and connects to the geometric interpretation of wedge/sliver states, with significant implications for tachyon condensation and D-brane physics.

Abstract

In a previous paper [hep-th/0012251] we proposed a simple class of actions for string field theory around the tachyon vacuum. In this paper we search for classical solutions describing D-branes of different dimensions using the ansatz that the solutions factorize into the direct product of a matter state and a universal ghost state. We find closed form expressions for the matter state describing D-branes of all dimensions. For the space filling D25-brane the state is the matter part of the zero angle wedge state, the ``sliver'', built in [hep-th/0006240]. For the other D-brane solutions the matter states are constructed using a solution generating technique outlined in [hep-th/0008252]. The ratios of tensions of various D-branes, requiring evaluation of determinants of infinite dimensional matrices, are calculated numerically and are in very good agreement with the known results.