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

Understand

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.