Reexamining Classical Solution and Tachyon Mode in Vacuum String Field Theory

TL;DR

This paper reevaluates the classical D25-brane solution and tachyon mode in vacuum string field theory, revealing violations in their equations under regularization and exploring implications for physical quantities like tachyon mass.

Contribution

It provides a detailed analysis of the oscillator construction's limitations and discusses potential resolutions for matching expected physical ratios.

Findings

Violations of equations in the level cut-off regularization.

Impact on tachyon mass and energy density ratios.

Discussion of possible solutions to reproduce expected ratios.

Abstract

We reexamine the oscillator construction of the D25-brane solution and the tachyon fluctuation mode of vacuum string field theory given previously. Both the classical solution and the tachyon mode are found to violate infinitesimally their determining equations in the level cut-off regularization. We study the effects of these violations on physical quantities such as the tachyon mass and the ratio of the energy density of the solution relative to the D25-brane tension. We discuss a possible way to resolve the problem of reproducing the expected value of one for the ratio.