Higher Level Open String States from Vacuum String Field Theory

TL;DR

This paper constructs higher-level open string states within Vacuum String Field Theory, confirming the eigenvalue conditions for correct mass spectra and addressing the removal of unwanted states through gauge fixing.

Contribution

It introduces a method to construct massive open string states using eigenvectors of projection operators with eigenvalue 1/2 in Vacuum String Field Theory.

Findings

Projection operators have eigenvalue 1/2 confirmed numerically.

Massive states can be constructed using specific eigenvectors.

Unwanted degenerate states can be gauged away.

Abstract

We construct massive open string states around a classical solution in the oscillator formulation of Vacuum String Field Theory. In order for the correct mass spectrum to be reproduced, the projection operators onto the modes of the left- and right-half of the string must have an anomalous eigenvalue 1/2, and the massive states are constructed using the corresponding eigenvector. We analyze numerically the projection operators by regularizing them to finite size matrices and confirm that they indeed have eigenvalue 1/2. Beside the desired massive states, we have spurious massive as well as massless states, which are infinitely degenerate. We show that these unwanted states can be gauged away.