Interior product, Lie derivative and Wilson line in the KBc subsector of open string field theory

The open string field theory of Witten (SFT) has a close formal similarity with Chern-Simons theory in three dimensions. This similarity is due to the fact that the former theory has concepts corresponding to forms, exterior derivative, wedge product and integration over the manifold. In this paper, we introduce the interior product and the Lie derivative in the KBc subsector of SFT. The interior product in SFT is specified by a two-component “tangent vector” and lowers the ghost number by one (like the ordinary interior product maps a p-form to (p − 1)-form). The Lie derivative in SFT is defined as the anti-commutator of the interior product and the BRST operator. The important property of these two operations is that they respect the KBc algebra.