Homotopy Operators and One-Loop Vacuum Energy at the Tachyon Vacuum

TL;DR

This paper constructs homotopy operators for the BRST operator in string field theory, demonstrating that the one-loop vacuum energy at the tachyon vacuum is moduli-independent, and revisits the cohomology problem with new tools.

Contribution

It introduces homotopy operators for the BRST operator in the context of the tachyon vacuum, providing new insights into vacuum energy and cohomology.

Findings

One-loop vacuum energy is moduli-independent.

Homotopy operators are constructed for the BRST operator.

Revisits cohomology problem with new methods.

Abstract

We construct the homotopy operators for the BRST operator in the theory around the identity-based solutions, which are believed to represent the tachyon vacuum in cubic bosonic open string field theory. Using the homotopy operators, we find that the one-loop vacuum energy at the tachyon vacuum is independent of moduli such as interbrane distances, which are included in the BRST operator. We also revisit the cohomology problem, which was solved earlier without the homotopy operators.