BRST Ghost-Vertex Operator in Witten's Cubic Open String Field Theory on Multiple $Dp$-branes

TL;DR

This paper investigates the BRST ghost field in Witten's cubic open string field theory on multiple Dp-branes, revealing its role as Faddeev-Popov ghosts ensuring non-Abelian gauge invariance.

Contribution

It demonstrates that the massless BRST ghost components act as Faddeev-Popov ghosts, preserving gauge invariance in non-Abelian Dp-brane configurations.

Findings

BRST ghost components serve as Faddeev-Popov ghosts

Maintains non-Abelian gauge invariance in string field theory

Extends ghost sector analysis to multiple Dp-branes

Abstract

The Becchi-Rouet-Stora-Tyutin (BRST) ghost field is a key element in constructing Witten's cubic open string field theory. However, to date, the ghost sector of the string field theory has not received a great deal of attention. In this study, we address the BRST ghost on multiple $Dp$-branes, which carries non-Abelian indices and couples to a non-Ablelian gauge field. We found that the massless components of the BRST ghost field can play the role of the Faddeev-Popov ghost in the non-Alelian gauge field, such that the string field theory maintains the local non-Abelian gauge invariance.