Fractional Supersymmetry and Minimal Coset Models in Conformal Field Theory

Chung, Stephen-wei; Lyman, Edwin; Tye, S.‐H. Henry

doi:10.1142/s0217751x92001484

Cited by 12 publications

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“…These algebras were conjectured [5,6,7] in the context of SU(2) coset constructions, and were presented as a new way of organizing 1 < c < 3 representations in CFT. Using a BRST cohomology approach [8] based on the fractional supersymmetry algebras, some details of the coset models have been worked out [9], while new coset models have been constructed [10]. These new coset models are SU(2) K ⊗ SU(2) L /SU(2) K+L where both K and L are rational; use of the fractional supersymmetry chiral algebras enables one to construct their branching functions.…”

Section: Introductionmentioning

confidence: 99%

Structure constants of the fractional supersymmetry chiral algebras

Argyres¹,

Grochocinski²,

Tye³

1991

Nuclear Physics B

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The fractional supersymmetry chiral algebras, A (K) , in two-dimensional conformal field theory are extended Virasoro algebras with fractional spin currents J (K) . We show that associativity and closure of A (K) determines its structure constants in the case that the Virasoro algebra is extended by precisely one current.We compute the structure constants of the A (K) algebras explicitly and we show that correlators of J (K) 's satisfy non-Abelian braiding relations.

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Section: Introductionmentioning

confidence: 99%

Structure constants of the fractional supersymmetry chiral algebras

Argyres¹,

Grochocinski²,

Tye³

1991

Nuclear Physics B

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“…In this section we derive the Kac and new determinant formulae for an arbitrary (integer) level K FSCA using the BRST operator [9,10] in a particular representation of FSCAs via a non-interacting theory of the Z K PF and a single boson with the background charge. Since by definition the Kac and new determinants for a given algebra are representation independent, our derivation is valid for all the representations of FSCAs with modules classified in section II.…”

Section: Derivation Of Kac and New Determinant Formulaementioning

confidence: 99%

“…The currents T (z) and G(z), defined in (3.2) and (3.7), generate the level K FSCA (2.11) for the values of the central charge c ≤ c 0 [6]. Now we consider the BRST operators [9,10]:…”

Section: )mentioning

confidence: 99%

“…In section III we derive the Kac and new determinant formulae using a generalization [9,10] of the BRST operator of Felder [11]. We also derive the relation between the Kac and new determinants.…”

Section: Introductionmentioning

confidence: 99%

“…We also derive the relation between the Kac and new determinants. The zeros of the Kac determinants were given in Ref [5,9,10]. To derive the Kac and new determinant formulae, we need to fix the orders of these zeros, as well as the zero mode contribution.…”

Section: Introductionmentioning

confidence: 99%

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Kac and new determinants for fractional superconformal algebras

Kakushadze

Tye

1994

Phys. Rev. D

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We derive the Kac and new determinant formulas 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 > 3 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 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-413 parafermion current algebra (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.PACS number(s): 11.25.Hf

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Construction of the K = 8 fractional superconformal algebras

1993

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We construct the K = 8 fractional superconformal algebras. There are two such extended Virasoro algebras, one of which was constructed earlier, involving a fractional spin (equivalently, conformal dimension) 6 5 current. The new algebra involves two additional fractional spin currents with spin 13 5 . Both algebras are nonlocal and satisfy non-abelian braiding relations. The construction of the algebras uses the isomorphism between the Z 8 parafermion theory and the tensor product of two tricritical Ising models. For the special value of the central charge c = 52 55 , corresponding to the eighth member of the unitary minimal series, the 13 5 currents of the new algebra decouple, while two spin 23 5 currents (level-2 current algebra descendants of the 13 5 currents) emerge. In addition, it is shown that the K = 8 algebra involving the spin 13 5 currents at central charge c = 12 5 is the appropriate algebra for the construction of the K = 8 (four-dimensional) fractional superstring.

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Fractional Supersymmetry and Minimal Coset Models in Conformal Field Theory

Abstract: Starting from fractional supersymmetry as an extended Virasoro algebra, we generalize Felder's BRST cohomology method to construct the characters and branching functions — in terms of string functions — of the SU(2) and SU(3) coset models, for both the unitary and nonunitary cases.

Cited by 12 publications

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Structure constants of the fractional supersymmetry chiral algebras

Structure constants of the fractional supersymmetry chiral algebras

Kac and new determinants for fractional superconformal algebras

Construction of the K = 8 fractional superconformal algebras

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