Zeeman Spectroscopy of the Star Algebra

TL;DR

This paper analytically solves for all eigenvalues and eigenvectors of the Neumann matrix in open bosonic string field theory, including zero modes and background B-field effects, providing explicit formulas and transcendental equations.

Contribution

It introduces a comprehensive analytical solution for the eigenproblem of the Neumann matrix with background B-field, including zero modes, which was previously unresolved.

Findings

Eigenvalues expressed as roots of transcendental equations

Explicit analytical expressions for eigenvectors

Inclusion of zero modes and background B-field effects

Abstract

We solve the problem of finding all eigenvalues and eigenvectors of the Neumann matrix of the matter sector of open bosonic string field theory, including the zero modes, and switching on a background B-field. We give the discrete eigenvalues as roots of transcendental equations, and we give analytical expressions for all the eigenvectors.