Kac and new determinants for fractional superconformal algebras

Journal Article · Fri Apr 15 00:00:00 EDT 1994 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.49.4122· OSTI ID:5094366

Kakushadze, Z; Tye, S H ^[1]

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1. Newman Laboratory of Nuclear Studies, Cornell University, Ithaca, New York 14853-5001 (United States)

We derive the Kac and new determinant formulas for an arbitrary (integer) level [ital K] fractional superconformal algebra using the BRST cohomology techniques developed in conformal field theory. In particular, we reproduce the Kac determinants for the Virasoro ([ital K]=1) and superconformal ([ital K]=2) algebras. For [ital 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 [ital K], we sketch the nonunitarity 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 formulas for the spin 4/3 parafermion current algebra (i.e., the [ital K]=4 fractional superconformal algebra) to the recently constructed three-dimensional flat Minkowski space-time representation of the spin-4/3 fractional superstring.

• OSTI ID: 5094366
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 49:8; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COMPOSITE MODELS
CONFORMAL GROUPS
CURRENT ALGEBRA
EXTENDED PARTICLE MODEL
FIELD THEORIES
LIE GROUPS
MATHEMATICAL MODELS
MATHEMATICAL SPACE
MINKOWSKI SPACE
PARTICLE MODELS
QUANTUM FIELD THEORY
QUARK MODEL
SPACE
SPACE-TIME
STRING MODELS
SU GROUPS
SU-2 GROUPS
SUPERSTRING MODELS
SYMMETRY
SYMMETRY GROUPS
UNITARY SYMMETRY