Star Algebra Spectroscopy

Abstract

The spectrum of the infinite dimensional Neumann matrices M^{11}, M^{12} and M^{21} in the oscillator construction of the three-string vertex determines key properties of the star product and of wedge and sliver states. We study the spectrum of eigenvalues and eigenvectors of these matrices using the derivation K_1 = L_1 + L_{-1} of the star algebra, which defines a simple infinite matrix commuting with the Neumann matrices. By an exact calculation of the spectrum of K_1, and by consideration of an operator generating wedge states, we are able to find analytic expressions for the eigenvalues and eigenvectors of the Neumann matrices and for the spectral density. The spectrum of M^{11} is continuous in the range [-1/3, 0) with degenerate twist even and twist odd eigenvectors for every eigenvalue except for -1/3.

LaTeX, 30 pages, 2 figures

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• Open String Star as a Continuous Moyal Product
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• Construction of the Vacuum String Field Theory on a non-BPS Brane
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• Towards Vacuum Superstring Field Theory: The Supersliver
• Four Lectures on Analytic Solutions in Open String Field Theory
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• Tachyon Condensation and Universal Solutions in String Field Theory
• The energy of the analytic lump solution in SFT
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• Vacuum String Field Theory with B field
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• Squeezed State Projectors in String Field Theory
• Continuous Half-String Representation of String Field Theory
• Moyal Formulation of Witten's Star Product in the Fermionic Ghost Sector
• Ghost story. I. Wedge states in the oscillator formalism
• Fermionic Ghosts in Moyal String Field Theory
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• Locality, Causality, and an Initial Value Formulation for Open String Field Theory
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• Exact time-localized solutions in Vacuum String Field Theory
• String Amplitudes from Moyal String Field Theory
• Higher Level Open String States from Vacuum String Field Theory
• String Field Theory Vertices, Integrability and Boundary States
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• Witten's Vertex Made Simple
• A fresh look at midpoint singularities in the algebra of string fields
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• Reexamining Classical Solution and Tachyon Mode in Vacuum String Field Theory
• Open Superstring Star as a Continuous Moyal Product
• Witten's Ghost Vertex Made Simple (bc and bosonized ghosts)
• D-branes as GMS Solitons in Vacuum String Field Theory
• Star Democracy in Open String Field Theory
• String Field Theory Projectors for Fermions of Integral Weight
• Normalization anomalies in level truncation calculations
• On surface states and star-subalgebras in string field theory
• Ghost story. III. Back to ghost number zero
• The Perturbative Spectrum of the Dressed Sliver
• Rolling Near the Tachyon Vacuum
• Zeeman Spectroscopy of the Star Algebra
• Time-localized projectors in String Field Theory with E-field
• Improved Off-Shell Scattering Amplitudes in String Field Theory and New Computational Methods
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• Lump solutions in SFT. Complements
• Ghost story. II. The midpoint ghost vertex
• Boundary and Midpoint Behaviors of Lump Solutions in Vacuum String Field Theory
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• Stretched strings in tachyon condensation models
• Towards open-closed string duality: Closed Strings as Open String Fields
• Fundamental strings in SFT
• Gauge Structure of Vacuum String Field Theory
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• Descent Relations in Cubic Superstring Field Theory
• Moyal Representation of the String Field Star Product in the Presence of a B-background
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