Half-strings, Projectors, and Multiple D-branes in Vacuum String Field Theory

TL;DR

This paper develops a mathematical framework in vacuum string field theory to construct and analyze projectors representing multiple D-branes, revealing deep connections with non-commutative solitons.

Contribution

It introduces a novel algebraic oscillator method to build higher rank projectors for multiple D-branes in vacuum string field theory.

Findings

Sliver state factors into left and right half-string functionals.

Higher rank projectors describe multiple D-branes at arbitrary positions.

Results show similarities with non-commutative solitons.

Abstract

A sliver state is a classical solution of the string field theory of the tachyon vacuum that represents a background with a single D25-brane. We show that the sliver wavefunctional factors into functionals of the left and right halves of the string, and hence can be naturally regarded as a rank-one projector in a space of half-string functionals. By developing an algebraic oscillator approach we are able construct higher rank projectors that describe configurations of multiple D-branes of various dimensionalities and located at arbitrary positions. The results bear remarkable similarities with non-commutative solitons.