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), Vol. 49:8; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

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