Spectral Flow and Feigin-Fuks Parameter Space of N=4 Superconformal Algebras

TL;DR

This paper explores the structure of N=4 superconformal algebras using spectral flow, revealing how automorphisms and unitary conditions shape their Feigin-Fuks representations.

Contribution

It provides a detailed analysis of the spectral flow's role in the Feigin-Fuks parameter space of N=4 superconformal algebras, including the incorporation of the $ta$ phase and automorphism relations.

Findings

Spectral flow acts as identity relations among generators.

Conditions for unitary representations are established.

Twisted fermions effectively incorporate the $ta$ phase.

Abstract

The parameter space of the Feigin-Fuks representations of the N=4 SU(2)$_k$ superconformal algebras is studied from the viewpoint of the specral flow. The $\eta$ phase of the spectral flow is nicely incorporated through twisted fermions and the spectral flow resulting from the inner automorphism of the N=4 superconformal algebras is explicitly shown to be operating as identiy relations among the generators. Conditions for the unitary representations are also investigated in our Feigin-Fuks parameter space.