Test of the Absence of Kinetic Terms around the Tachyon Vacuum in Cubic String Field Theory

TL;DR

This paper investigates whether the non-perturbative tachyon vacuum in cubic open string field theory lacks open string dynamics by examining the kinetic terms of scalar fluctuations, supporting the conjecture of their absence.

Contribution

It provides evidence that scalar fluctuations around the tachyon vacuum do not have kinetic terms, supporting the idea of no open string dynamics at this vacuum in cubic string field theory.

Findings

Kinetic terms for scalar modes vanish near the tachyon vacuum.

BRST invariance of scalar components is maintained without kinetic terms.

Supports the conjecture of no open string excitations at the tachyon vacuum.

Abstract

It has been conjectured that the bosonic open string theory around the non-perturbative tachyon vacuum has no open string dynamics at all. We explore, in the cubic open string field theory with level truncation approximation, the possibility that this conjecture is realized by the absence of kinetic terms of the string field fluctuations. We study the kinetic terms with two and four derivatives for the lower level scalar modes as well as their BRST transformation properties. The behavior of the coefficients of the kinetic terms in the neighborhood of the non-perturbative vacuum supports our expectation that the BRST invariant scalar component lacks its kinetic term.