Fractional supersymmetry in conformal field theory and string theory

Miscellaneous · Wed Jan 01 00:00:00 EST 1992

OSTI ID:7271660

Lyman, E S

The author studies the structure of the fractional superconformal algebras. These are generalizations of the ordinary superconformal algebra, which generate a symmetry between bosonic fields and parafermionic fields of fraction spin. It is shown that the SU(2) minimal coset conformal field theories have fractional supersymmetry by explicity constructing the irreducible representations of the algebra, employing a generalization of the BRST cohomology method introduced by Felder. The author calculates the characters and branching functions of the irreducible representations and shows they agree with the known results for SU(2) coset models in the unitary case. It is shown how this method can be extended to study the irreducible representations of SU(N) minimal coset models (N>2), without detailed knowledge of the structures of the symmetry algebra. String theories are studied with world-sheet fraction supersymmetry, restricting the study to the SU(2), K = 4 case. The K = 4 fractional superstring Fock space is constructed in terms of Z[sub 4] parafermions and free bosons. Employing a bosonization of the parafermion theory, the author computes the operator product emission of the primary fields, and obtains the generalized commutation relations satisfied by the modes of these fields. The representation of string theory is considered in which the Fock space is larger than the Lorentz-covariant one indicated by the fractional superstring partition function. The form is derived of the fractional superconformal algebra appropriate for the tensor product theory that may generate the constraint algebra for the physical states of the fractional superstring. Issues concerning the associativity, modings and braiding properties of the fraction superconformal algebra are discussed. The use of the constraint algebra to obtain the physical state conditions that the spectrum must satisfy is illustrated by an application to the massless states of the K = 4 fractional superstring.

• Research Organization: Cornell Univ., Ithaca, NY (United States)
• OSTI ID: 7271660
• Resource Relation: Other Information: Thesis (Ph.D.)
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
SUPERSYMMETRY
ALGEBRAIC FIELD THEORY
STRING MODELS
CONFORMAL GROUPS
SU GROUPS
AXIOMATIC FIELD THEORY
COMPOSITE MODELS
EXTENDED PARTICLE MODEL
FIELD THEORIES
LIE GROUPS
MATHEMATICAL MODELS
PARTICLE MODELS
QUANTUM FIELD THEORY
QUARK MODEL
SYMMETRY
SYMMETRY GROUPS
662120* - General Theory of Particles & Fields- Symmetry
Conservation Laws
Currents & Their Properties- (1992-)