Construction of the K=8 Fractional Superconformal Algebras

Details Construction of the K=8 Fractional Superconformal Algebras Construction of the K=8 Fractional Superconformal Algebras

1992-02-03

arxiv.org/abs/hep-th/9202007v1

Nucl.Phys. B391 (1993) 409-462

Physics

High Energy Physics

High Energy Physics - Theory

53 pages (or 82/2 = 41 pages in reduced format)

Scientific paper

10.1016/0550-3213(93)90154-H

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.

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