Witten's Vertex Made Simple
High Energy Physics - Theory
2009-11-10 v3
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.
Cite
@article{arxiv.hep-th/0304158,
title = {Witten's Vertex Made Simple},
author = {D. Belov and C. Lovelace},
journal= {arXiv preprint arXiv:hep-th/0304158},
year = {2009}
}
Comments
24 pages, 2 figures, RevTeX style, typos corrected