Fermionic Ghosts in Moyal String Field Theory

TL;DR

This paper completes the fermionic ghost sector in Moyal string field theory by constructing a consistent map, regularization scheme, and deriving ghost coefficients, enabling explicit calculations of string interactions.

Contribution

It introduces a detailed construction of the fermionic ghost sector in Moyal string field theory, including a new regularization scheme and explicit derivation of ghost coefficients.

Findings

Ghost Neumann coefficients satisfy Gross-Jevicki relations

Derived off-shell four-point tachyon function with ghost contributions

Validated the formalism by matching conformal field theory results

Abstract

We complete the construction of the Moyal star formulation of bosonic open string field theory (MSFT) by providing a detailed study of the fermionic ghost sector. In particular, as in the case of the matter sector, (1) we construct a map from Witten's star product to the Moyal product, (2) we propose a regularization scheme which is consistent with the matter sector and (3) as a check of the formalism, we derive the ghost Neumann coefficients algebraically directly from the Moyal product. The latter satisfy the Gross-Jevicki nonlinear relations even in the presence of the regulator, and when the regulator is removed they coincide numerically with the expression derived from conformal field theory. After this basic construction, we derive a regularized action of string field theory in the Siegel gauge and define the Feynman rules. We give explicitly the analytic expression of the off-shell four point function for tachyons, including the ghost contribution. Some of the results in this paper have already been used in our previous publications. This paper provides the technical details of the computations which were omitted there.