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

TL;DR

This paper introduces interior product and Lie derivative concepts into the $KBc$ subsector of open string field theory, enabling the construction of Wilson lines that may help analyze fluctuation modes around multi-brane solutions.

Contribution

It defines interior product and Lie derivative in the $KBc$ subsector of SFT, extending the algebra and enabling new geometric constructions like Wilson lines.

Findings

Defined interior product and Lie derivative in $KBc$ SFT

Constructed the $KBc$ manifold via Lie derivative deformation

Built Wilson line to analyze fluctuation modes around multi-brane solutions

Abstract

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. Deforming the original $(K,B,c)$ by using the Lie derivative, we can consider an infinite copies of the $KBc$ algebra, which we call the $KBc$ manifold. As an application, we construct the Wilson line on the manifold, which could play a role in reproducing degenerate fluctuation modes around a multi-brane solution.