Time-localized projectors in String Field Theory with E-field

TL;DR

This paper extends string field theory analysis to include a constant electric field, demonstrating time localization of solutions and exploring how the electric field influences the lifetime of unstable solitons.

Contribution

It introduces a method to analyze time localization in the presence of an electric field and constructs a normalized basis in a background with a B-field.

Findings

Time localization persists with electric field inclusion.

Soliton lifetime depends on electric field and b-parameter.

Constructed a normalized diagonal basis in B-field background.

Abstract

We extend the analysis of hep-th/0409063 to the case of a constant electric field turned on the worldvolume and on a transverse direction of a D-brane. We show that time localization is still obtained by inverting the discrete eigenvalues of the lump solution. The lifetime of the unstable soliton is shown to depend on two free parameters: the b-parameter and the value of the electric field. As a by-product, we construct the normalized diagonal basis of the star algebra in $B_{\mu\nu}$-field background.