Z2 x Z2 graded superconformal algebra of parafermionic type

TL;DR

This paper introduces a novel Z2 x Z2 graded superconformal algebra generated by three N=1 superconformal algebras interconnected through parafermionic relations, with discussions on its representation theory and potential infinite series.

Contribution

It presents a new conformal algebra structure with parafermionic relations and explores its representation theory and possible infinite series of related algebras.

Findings

New Z2 x Z2 graded superconformal algebra introduced

Representation theory and unitary models discussed

Conjecture on infinite series of parafermionic algebras with superconformal subalgebras

Abstract

We present a new conformal algebra. It is Z2 x Z2 graded and generated by three N=1 superconformal algebras coupled to each other by nontrivial relations of parafermionic type. The representation theory and unitary models of the algebra are briefly discussed. We also conjecture the existence of infinite series of parafermionic algebras containing many N=1 or N=2 superconformal subalgebras.