Construction of the K=8 Fractional Superconformal Algebras

TL;DR

This paper constructs two new non-local fractional superconformal algebras with spins 6/5 and 13/5, using parafermion and minimal model theories, relevant for fractional superstring models.

Contribution

It introduces a novel K=8 fractional superconformal algebra involving additional fractional spin currents and explores their properties and applications in superstring theory.

Findings

Two extended Virasoro algebras with fractional spins constructed.

At c=52/55, certain currents decouple, revealing simpler algebraic structures.

The K=8 algebra with spin 13/5 currents is suitable for fractional superstring models.

Abstract

We construct the K=8 fractional superconformal algebras. There are two such extended Virasoro algebras, one of which was constructed earlier, involving a fractional spin (equivalently, conformal dimension) 6/5 current. The new algebra involves two additional fractional spin currents with spin 13/5. Both algebras are non-local and satisfy non-abelian braiding relations. The construction of the algebras uses the isomorphism between the Z_8 parafermion theory and the tensor product of two tricritical Ising models. For the special value of the central charge c=52/55, corresponding to the eighth member of the unitary minimal series, the 13/5 currents of the new algebra decouple, while two spin 23/5 currents (level-2 current algebra descendants of the 13/5 currents) emerge. In addition, it is shown that the K=8 algebra involving the spin 13/5 currents at central charge c=12/5 is the appropriate algebra for the construction of the K=8 (four-dimensional) fractional superstring.