Boundary CFT Construction of D-branes in Vacuum String Field Theory

TL;DR

This paper constructs classical solutions for all D-branes in any fixed 2D CFT background within vacuum string field theory, using boundary CFT techniques and the sliver state to match D-brane tensions.

Contribution

It extends previous D-brane solutions to arbitrary backgrounds using boundary CFT and geometrical sliver states, clarifying tension ratios and spectrum reproduction.

Findings

Successfully constructed D-brane solutions in general boundary CFTs

Derived correct D-brane tension ratios from sliver state norms

Explored spectrum of physical states as deformations of the sliver

Abstract

In previous papers we built (multiple) D-branes in flat space-time as classical solutions of the string field theory based on the tachyon vacuum. In this paper we construct classical solutions describing all D-branes in any fixed space-time background defined by a two-dimensional CFT of central charge 26. A key role is played by the geometrical definition of the sliver state in general boundary CFT's. The correct values for ratios of D-brane tensions arise because the norm of the sliver solution is naturally related to the disk partition function of the appropriate boundary CFT. We also explore the possibility of reproducing the known spectrum of physical states on a D-brane as deformations of the sliver.