BV Analysis of Tachyon Fluctuation around Multi-brane Solutions in Cubic String Field Theory

TL;DR

This paper investigates the physicality of tachyon fluctuations around multi-brane solutions in cubic string field theory using the BV formalism, revealing degeneracy patterns that distinguish between 2-brane and vacuum solutions.

Contribution

It applies the BV formalism to analyze tachyon modes in string field theory, providing insights into their physical relevance on different solutions.

Findings

Degeneracy of the anti-bracket matrix indicates physical tachyon modes on the 2-brane.

Non-degeneracy of the matrix corresponds to unphysical tachyon modes on the vacuum.

Results align with theoretical expectations for pure-gauge solutions.

Abstract

We study whether the tachyon mode exists as a physical fluctuation on the 2-brane solution and on the tachyon vacuum solution in cubic open string field theory. Our analysis is based on the Batalin-Vilkovisky formalism. We first construct a set of six string states which corresponds to the set of fields and anti-fields containing the tachyon field. Whether the tachyon field can exist as a physical fluctuation is determined by the 6x6 matrix defining the anti-bracket in the present sector. If the matrix is degenerate/non-degenerate, the tachyon field is physical/unphysical. Calculations for the pure-gauge type solutions in the framework of the KBc algebra and using the Ke-regularization lead to the expected results. Namely, the matrix for the anti-bracket is degenerate/non-degenerate in the case of the 2-brane/tachyon-vacuum solution. Our analysis is not complete, in particular, in that we have not identified the four-fold degeneracy of tachyon fluctuation on the 2-brane solution, and moreover that the present six states do not satisfy the hermiticity condition.