Closed string deformations in open string field theory I: bosonic string

TL;DR

This paper explores how deformations in open string field theory, specifically in the bosonic string, lead to vacuum shifts that accommodate changes in closed string backgrounds, affecting open string spectra and interactions.

Contribution

It introduces a gauge invariant deformation of open string field theory with the Witten star product, analyzing vacuum solutions and their effects on open string modes in deformed backgrounds.

Findings

Vacuum-shift solutions cancel the tadpole destabilization.

Deformation changes the mass spectrum of open string modes.

Open string propagator can mitigate closed string degenerations.

Abstract

This is the first of a series of three papers on open string field theories based on Witten star product deformed with a gauge invariant open/closed coupling. This deformation is a tree-level tadpole which destabilizes the initial perturbative vacuum. We discuss the existence of vacuum-shift solutions which cancel the tadpole and represent a new configuration where the initial D-brane system has adapted to the change in the closed string background. As an example we consider the bulk deformation which changes the compactification radius and, to first order in the deformation, we reproduce the shift in the mass of the open string KK modes from the new kinetic operator after the vacuum shift. We also discuss the possibility of taming closed string degenerations with the open string propagator in the simplest amplitude corresponding to two closed strings off a disk.