Tachyon Vacuum of Bosonic Open String Field Theory in Marginally Deformed Backgrounds

TL;DR

This paper constructs the tachyon vacuum solution in bosonic open string field theory within marginally deformed backgrounds, showing that the vacuum energy remains unchanged and gauge invariants are affected as expected, confirming properties of identity-based marginal solutions.

Contribution

It introduces a new set of string fields satisfying the KBc algebra in marginally deformed backgrounds, enabling the construction of the tachyon vacuum solution with consistent vacuum energy and gauge invariants.

Findings

Vacuum energy density matches the undeformed case.

Gauge invariant overlap varies with marginal deformations.

Vacuum energy is zero for identity-based marginal solutions.

Abstract

We consider bosonic open string field theory in marginally deformed backgrounds, which is obtained by expanding the string field around the identity-based solutions associated with marginal deformations. We find a new set of string fields which satisfies the KBc algebra, but the nilpotent kinetic operator is that of the theory expanded around the identity-based marginal solution. By use of these string fields, we construct the tachyon vaccum solution in marginally deformed backgrounds. The vacuum energy density is equivalent to that of the tachyon vacuum without marginal deformations. The gauge invariant overlap is changed according to the effect of marginal deformations, as expected from known results in CFT. These results suggest that the vacuum energy is zero for the identity-based marginal solutions in the original theory.