Split string field theory II

TL;DR

The paper advances a split-string, operator-based formulation of open string field theory in the ghost sector by leveraging bosonized ghosts and a class of pure ghost BRST operators $Q_f$ that satisfy the theory’s axioms when acting on well-behaved states. It demonstrates that ghost-projected states can solve the ghost part of the equations of motion and constructs ghost-sector solutions whose action vanishes in this framework, prompting discussion of potential interpretations and extensions. The work connects these ghost constructions to matter-sector projector states, suggesting a path to describe multiple D-brane configurations in the RSZ vacuum, and discusses how the full theory with BRST operator $Q_B$ might be approached, including midpoint anomalies and potential nonzero actions. Overall, it provides a concrete, background-independent algebraic framework for open string field theory, laying groundwork for incorporating closed-string physics and exploring observables via the eigenvalues of a covariant derivative. The results illuminate how pure ghost dynamics could underpin the decoupling of open strings in the closed-string vacuum and point to future directions in analytic solutions and level-truncation studies.

Abstract

We describe the ghost sector of cubic string field theory in terms of degrees of freedom on the two halves of a split string. In particular, we represent a class of pure ghost BRST operators as operators on the space of half-string functionals. These BRST operators were postulated by Rastelli, Sen, and Zwiebach to give a description of cubic string field theory in the closed string vacuum arising from condensation of a D25-brane in the original tachyonic theory. We find a class of solutions for the ghost equations of motion using the pure ghost BRST operators. We find a vanishing action for these solutions, and discuss possible interpretations of this result. The form of the solutions we find in the pure ghost theory suggests an analogous class of solutions in the original theory on the D25-brane with BRST operator Q_B coupling the matter and ghost sectors.