Observables as Twist Anomaly in Vacuum String Field Theory

TL;DR

This paper uncovers a new mathematical structure in vacuum string field theory observables, showing how twist degeneracy breakdown at eigenvalue edges leads to non-zero physical quantities, and suggests the classical solution corresponds to two D25-branes.

Contribution

It introduces a novel twist anomaly framework explaining non-vanishing observables in vacuum string field theory and provides a method for their correct calculation.

Findings

Observables are linked to twist degeneracy breakdown at eigenvalue edges.

Numerical results suggest the solution describes two D25-branes.

A general prescription for simplifying observable expressions is proposed.

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.