Split string field theory II

TL;DR

This paper explores the ghost sector of cubic string field theory using half-string degrees of freedom, introduces pure ghost BRST operators, and finds solutions with vanishing action, providing insights into the vacuum structure of string theory.

Contribution

It represents pure ghost BRST operators as operators on half-string functionals and finds solutions with zero action, advancing understanding of the ghost sector in string field theory.

Findings

Pure ghost BRST operators can be represented on half-string functionals.

Solutions with vanishing action are found for the ghost equations of motion.

The form of solutions suggests analogous solutions in the original theory with matter-ghost coupling.

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.