Split string field theory I

TL;DR

This paper introduces projection operators in matter sector of string field theory using half-string modes, advancing towards analytic solutions and D-brane configurations.

Contribution

It presents a method to construct projection operators in matter sector, enabling analytic solutions and multi D-brane configurations in string field theory.

Findings

Projection operators are constructed as rank one operators related to the sliver state.

Higher rank projection operators are developed for multiple D-brane configurations.

The approach advances understanding of solutions in string field theory with pure ghost BRST operator.

Abstract

We describe projection operators in the matter sector of Witten's cubic string field theory using modes on the right and left halves of the string. These projection operators represent a step towards an analytic solution of the equations of motion of the full string field theory, and can be used to construct Dp-brane solutions of the string field theory when the BRST operator Q is taken to be pure ghost, as suggested in the recent conjecture by Rastelli, Sen and Zwiebach. We show that a family of solutions related to the sliver state are rank one projection operators on the appropriate space of half-string functionals, and we construct higher rank projection operators corresponding to configurations of multiple D-branes.