Pure Gauge Configurations and Tachyon Solutions to String Field Theories Equations of Motion

TL;DR

This paper investigates the convergence issues of pure gauge configurations in open string field theories and demonstrates that additional terms are needed to satisfy the equations of motion, supporting the Sen conjectures.

Contribution

It provides a numerical analysis showing divergence in pure gauge configurations and proposes adding extra terms to ensure convergence and validity of solutions.

Findings

Pure gauge configurations diverge at large parameters on wedge state subspace.

Adding extra terms to the perturbation expansion cures divergence.

Numerical evidence supports the validity of the modified solutions in string field theory.

Abstract

In constructions of analytical solutions to open string field theories pure gauge configurations parameterized by wedge states play an essential role. These pure gauge configurations are constructed as perturbation expansions and to guaranty that these configurations are asymptotical solutions to equations of motions one needs to study convergence of the perturbation expansions. We demonstrate that for the large parameter of the perturbation expansion these pure gauge truncated configurations give divergent contributions to the equation of motion on the subspace of the wedge states. We perform this demonstration numerically for the pure gauge configurations related to tachyon solutions for the bosonic and the NS fermionic SFT. By the numerical calculations we also show that the perturbation expansions are cured by adding extra terms. These terms are nothing but the terms necessary to make valued the Sen conjectures.