Kac and New Determinants for Fractional Superconformal Algebras

Abstract

We derive the Kac and new determinant formulae for an arbitrary (integer) level $K$ fractional superconformal algebra using the BRST cohomology techniques developed in conformal field theory. In particular, we reproduce the Kac determinants for the Virasoro ($K=1$) and superconformal ($K=2$) algebras. For $K\ge 3$ there always exist modules where the Kac determinant factorizes into a product of more fundamental new determinants. Using our results for general $K$, we sketch the non-unitarity proof for the $SU(2)$ minimal series; as expected, the only unitary models are those already known from the coset construction. We apply the Kac determinant formulae for the spin-4/3 parafermion current algebra ({\em i.e.}, the $K=4$ fractional superconformal algebra) to the recently constructed three-dimensional flat Minkowski space-time representation of the spin-4/3 fractional superstring. We prove the no-ghost theorem for the space-time bosonic sector of this theory; that is, its physical spectrum is free of negative-norm states.

33 pages, Revtex 3.0, Cornell preprint CLNS 93/1243

References in corpus (4)

• Central Charge Reduction and Spacetime Statistics in the Fractional Superstring
• Aspects of Fractional Superstrings
• Heterotic Parafermionic Superstring
• Tree scattering amplitudes of the spin-4/3 fractional superstring II: the twisted sectors

Cited by in corpus (7)

• Coset conformal blocks and N=2 gauge theories
• Coset conformal field theory and instanton counting on C^2/Z_p
• Fractional supersymmetric Liouville theory and the multi-cut matrix models
• Tree scattering amplitudes of the spin-4/3 fractional superstring II: the twisted sectors
• Tree scattering amplitudes of the spin-4/3 fractional superstring I: the untwisted sectors
• Status of Fractional Superstrings
• Fractional Supersymmetry As a Matrix Model