Observables as Twist Anomaly in Vacuum String Field Theory

TL;DR

This paper reframes key VSFT observables—the tachyon mass and energy density—through the lens of twist anomaly, showing that naively vanishing twist-degenerate contributions are rescued by edge singularities at $\lambda=-1/3$ in the Neumann data spectrum. It introduces a careful deformation prescription to regulate observables like $G$ and $H$ while respecting edge singularities, thereby recovering correct tachyon-mass behavior and a consistent energy-density result. Numerical analysis, with these refinements, indicates the VSFT classical solution represents two D25-branes rather than one, highlighting subtle cancellations in determinant factors and the importance of edge effects. The work lays groundwork for a more robust connection between VSFT solutions and multi-brane configurations, and it points to further directions toward analytic eigenvalue distributions and potential emergence of closed strings as twist anomalies.

Abstract

We reveal a novel mathematical structure in physical observables, the mass of tachyon fluctuation mode and the energy density, associated with a classical solution of vacuum string field theory constructed previously [hep-th/0108150]. We find that they are expressed in terms of quantities which apparently vanish identically due to twist even-odd degeneracy of eigenvalues of a Neumann coefficient matrix defining the three-string interactions. However, they can give non-vanishing values because of the breakdown of the degeneracy at the edge of the eigenvalue distribution. We also present a general prescription of correctly simplifying the expressions of these observables. Numerical calculation of the energy density following our prescription indicates that the present classical solution represents the configuration of two D25-branes.