Split string field theory I

TL;DR

The paper develops a half-string formalism for the matter sector of Witten's cubic open string field theory and shows that string fields can be represented as operators on half-string functionals. It identifies Gaussian half-string states that satisfy projection conditions, proving that the D-instanton sliver is a rank-one projector and demonstrating how to construct higher-rank projections corresponding to multiple D-branes. The work provides explicit prescriptions for generating single and multi-brane configurations as projection operators and analyzes normalizability and gauge equivalence aspects. This analytic framework offers a path toward solving the full string field theory and motivates extending the construction to the ghost sector in future work, potentially clarifying the brane physics in the RSZ scenario.

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.