Numerical Solutions of Open String Field Theory in Marginally Deformed Backgrounds

TL;DR

This paper numerically investigates open string field theory solutions in marginally deformed backgrounds, confirming the vanishing energy of identity-based solutions and analyzing the behavior of vacuum and marginal branches.

Contribution

It provides the first detailed numerical analysis of open string field theory in marginally deformed backgrounds, including vacuum energy and gauge invariant overlaps.

Findings

Vacuum energy cancels D-brane tension at higher truncation levels.

Identity-based marginal solutions have vanishing energy regardless of parameter.

Finite bound observed for the massless field in deformed backgrounds.

Abstract

We investigate numerical solutions of bosonic open string field theory in some marginally deformed backgrounds, which are obtained by expanding the action around an identity-based marginal solution with one parameter. We construct numerical solutions in the Siegel gauge and the Landau gauge corresponding to the tachyon vacuum. Their vacuum energy approximately cancels the D-brane tension for larger intervals of the parameter with increasing truncation level. The result is consistent with the previous expectation that the identity-based marginal solution has vanishing energy regardless of the values of the parameter. We also study the marginal branch (M-branch) and the vacuum branch (V-branch) and evaluate not only the vacuum energy but also the gauge invariant overlaps with the graviton and the closed tachyon. We observe that there is a finite bound for the value of the massless field of numerical solutions even in the marginally deformed background.