Diagonal Representation of Open String Star and Moyal Product

TL;DR

This paper derives a diagonal representation of the 3-string vertices in open string field theory, revealing Moyal structures and both continuous and discrete non-commutativity parameters in matter and ghost sectors.

Contribution

It explicitly finds the spectrum of key operators and provides a diagonal representation of the star-product, uncovering new Moyal structures and non-commutativity parameters.

Findings

Spectrum of operators $M^{rs}$ and $ ilde{M}^{rs}$ determined.

Diagonal representation of 3-string vertices derived.

Identification of continuous and discrete non-commutativity parameters.

Abstract

We explicitly find the spectrum of the operators $M^{rs}$ and $\widetilde{M}^{rs}$, which specify the star-product in the matter and ghost sectors correspondingly. Further we derive the diagonal representation for the 3-string vertices. Using this representation we identify the appearing Moyal structures in the matter sector. In addition to the continuous non-commutativity parameter $\theta(\kappa)$ found in hep-th/0202087 we find the discrete non-commutativity parametrized by $\theta_{\xi}$.