Spectral properties of ghost Neumann matrices

TL;DR

This paper investigates the spectral properties of ghost Neumann matrices in string theory, proposing a new reconstruction method that requires additional boundary data, supporting the existence of a ghost three-string vertex similar to the matter vertex.

Contribution

It introduces a novel heuristic formula for reconstructing ghost Neumann matrices from eigenvalues and eigenvectors, highlighting the need for boundary data and supporting the ghost three-string vertex conjecture.

Findings

Traditional spectral representation is invalid for ghost matrices.

A new heuristic formula for reconstruction is proposed.

Supports the existence of a ghost three-string vertex.

Abstract

We continue the analysis of the ghost wedge states in the oscillator formalism by studying the spectral properties of the ghost matrices of Neumann coefficients. We show that the traditional spectral representation is not valid for these matrices and propose a new heuristic formula that allows one to reconstruct them from the knowledge of their eigenvalues and eigenvectors. It turns out that additional data, which we call boundary data, are needed in order to actually implement the reconstruction. In particular our result lends support to the conjecture that there exists a ghost three strings vertex with properties parallel to those of the matter three strings vertex.