Witten’s vertex made simple

2003/04/30 by D.M. Belov, D. Belov, C. Lovelace · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Quantum chaos and dynamical systems #Theoretical and Computational Physics #hep-th

paper · pdf · doi:10.1103/physrevd.68.066003

published as Phys.Rev. D68 (2003) 066003 · 24 pages, 2 figures, RevTeX style, typos corrected

arxiv created 2003/07/02 · openalex publication_date 2003/09/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Diagonal Representation of Open String Star and Moyal Product
• K-Theory from a physical perspective
• Moyal Formulation of Witten's Star Product in the Fermionic Ghost Sector
• Irreducible Unitary Representations of the Lorentz Group
• Virasoro operators in the continuous basis of string field theory

Cited by

• Witten’s ghost vertex made simple