$\Bbb {Z}_2$ x $\Bbb {Z}_2$ graded superconformal algebra of parafermionic type

Abstract

We present a new conformal algebra. It is $\Bbb {Z}_2$ x $\Bbb {Z}_2$ 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.