Witten's Vertex Made Simple

Abstract

The infinite matrices in Witten's vertex are easy to diagonalize. It just requires some SL(2,R) lore plus a Watson-Sommerfeld transformation. We calculate the eigenvalues of all Neumann matrices for all scale dimensions s, both for matter and ghosts, including fractional s which we use to regulate the difficult s=0 limit. We find that s=1 eigenfunctions just acquire a p term, and x gets replaced by the midpoint position.

24 pages, 2 figures, RevTeX style, typos corrected

References in corpus (5)

• K-Theory from a physical perspective
• Diagonal Representation of Open String Star and Moyal Product
• Virasoro operators in the continuous basis of string field theory
• On Continuous Moyal Product Structure in String Field Theory
• Moyal Formulation of Witten's Star Product in the Fermionic Ghost Sector

Cited by in corpus (15)

• Four Lectures on Analytic Solutions in Open String Field Theory
• Continuous Half-String Representation of String Field Theory
• Ghost story. I. Wedge states in the oscillator formalism
• Locality, Causality, and an Initial Value Formulation for Open String Field Theory
• Star Democracy in Open String Field Theory
• A Note on kappa-Diagonal Surface States
• Witten's Ghost Vertex Made Simple (bc and bosonized ghosts)
• String Field Theory Projectors for Fermions of Integral Weight
• Ghost story. III. Back to ghost number zero
• Rolling Near the Tachyon Vacuum
• Improved Off-Shell Scattering Amplitudes in String Field Theory and New Computational Methods
• Ghost story. II. The midpoint ghost vertex
• Symplectic structure in open string field theory I: Rolling tachyons
• Spectral properties of ghost Neumann matrices
• Descent Relations in Cubic Superstring Field Theory