Pseudo Cuntz Algebra and Recursive FP Ghost System in String Theory

TL;DR

This paper introduces the pseudo Cuntz algebra to represent FP ghost systems in string theory, providing new recursive embedding methods and connecting to known representations of ghost zero-modes.

Contribution

It generalizes the recursive fermion system using the pseudo Cuntz algebra to embed FP ghost algebra in string theory, revealing new representation structures.

Findings

Representation of FP ghosts matches known four-dimensional case.

Another representation corresponds to a two-dimensional ghost zero-mode case.

Introduces recursive embedding methods for ghost algebra in indefinite-metric spaces.

Abstract

Representation of the algebra of FP (anti)ghosts in string theory is studied by generalizing the recursive fermion system in the Cuntz algebra constructed previously. For that purpose, the pseudo Cuntz algebra, which is a $\ast$-algebra generalizing the Cuntz algebra and acting on indefinite-metric vector spaces, is introduced. The algebra of FP (anti)ghosts in string theory is embedded into the pseudo Cuntz algebra recursively in two different ways. Restricting a certain permutation representation of the pseudo Cuntz algebra, representations of these two recursive FP ghost systems are obtained. With respect to the zero-mode operators of FP (anti)ghosts, it is shown that one corresponds to the four-dimensional representation found recently by one of the present authors (M.A.) and Nakanishi, while the other corresponds to the two-dimensional one by Kato and Ogawa.