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arXiv · hep-th/9310160

Kac and New Determinants for Fractional Superconformal Algebras

Zurab Kakushadze·S. -H. Henry Tye
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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 $K\geq3$ 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.

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Zurab Kakushadze, S. -H. Henry Tye. 1993-10-24. Kac and New Determinants for Fractional Superconformal Algebras. https://doi.org/10.1103/physrevd.49.4122

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