Gauge-invariant observables and marginal deformations in open string field theory

TL;DR

This paper investigates the relationship between gauge-invariant observables and marginal deformations in open string field theory, revealing that solutions form a finite branch consistent with the fundamental domain of the moduli space.

Contribution

It constructs a map between boundary conformal field theory parameters and open string solutions using gauge-invariant observables and confirms the finite solution range through numerical analysis.

Findings

Solutions exist only within a finite range of the marginal field.

Gauge-invariant observables align with the energy-momentum tensor analysis.

Results support the finite branch covering one fundamental domain of the moduli space.

Abstract

The level-truncation analysis of open string field theory for a class of periodic marginal deformations indicates that a branch of solutions in Siegel gauge exists only for a finite range of values of the marginal field. The periodicity in the deformation parameter is thus obscure. We use the relation between gauge-invariant observables and the closed string tadpole on a disk conjectured by Ellwood to construct a map between the deformation parameter of the boundary conformal field theory and the parameter labeling classical solutions of open string field theory. We evaluate the gauge-invariant observables for the numerical solutions in Siegel gauge up to level 12 and find that our results qualitatively agree with the analysis by Sen using the energy-momentum tensor and are consistent with the picture that the finite range of the branch covers one fundamental domain of the periodic moduli space.