Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-10-24
Phys.Rev. D49 (1994) 4122-4138
Physics
High Energy Physics
High Energy Physics - Theory
33 pages, Revtex 3.0, Cornell preprint CLNS 93/1243
Scientific paper
10.1103/PhysRevD.49.4122
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.
Henry Tye S.-H.
Kakushadze Zurab
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