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The open string field theory of Witten (SFT) has a close formal similaritywith Chern-Simons theory in three dimensions. This similarity is due to thefact that the former theory has concepts corresponding to forms, exteriorderivative, wedge product and integration over the manifold. In this paper, weintroduce the interior product and the Lie derivative in the $KBc$ subsector ofSFT. The interior product in SFT is specified by a two-component "tangentvector" and lowers the ghost number by one (like the ordinary interior productmaps a $p$-form to $(p-1)$-form). The Lie derivative in SFT is defined as theanti-commutator of the interior product and the BRST operator. The importantproperty of these two operations is that they respect the $KBc$ algebra.Deforming the original $(K,B,c)$ by using the Lie derivative, we can consideran infinite copies of the $KBc$ algebra, which we call the $KBc$ manifold. Asan application, we construct the Wilson line on the manifold, which could playa role in reproducing degenerate fluctuation modes around a multi-branesolution.

Interior Product, Lie Derivative and Wilson Line in the $KBc$ Subsector of Open String Field Theory