Tree scattering amplitudes of the spin-4/3 fractional superstring I: the untwisted sectors

Abstract

Scattering amplitudes of the spin-4/3 fractional superstring are shown to satisfy spurious state decoupling and cyclic symmetry (duality) at tree-level in the string perturbation expansion. This fractional superstring is characterized by the spin-4/3 fractional superconformal algebra---a parafermionic algebra studied by Zamolodchikov and Fateev involving chiral spin-4/3 currents on the world-sheet in addition to the stress-energy tensor. Examples of tree scattering amplitudes are calculated in an explicit c=5 representation of this fractional superconformal algebra realized in terms of free bosons on the string world-sheet. The target space of this model is three-dimensional flat Minkowski space-time with a level-2 Kac-Moody so(2,1) internal symmetry, and has bosons and fermions in its spectrum. Its closed string version contains a graviton in its spectrum. Tree-level unitarity (i.e., the no-ghost theorem for space-time bosonic physical states) can be shown for this model. Since the critical central charge of the spin-4/3 fractional superstring theory is 10, this c=5 representation cannot be consistent at the string loop level. The existence of a critical fractional superstring containing a four-dimensional space-time remains an open question.

42 pages, 4 figures, latex, IASSNS-HEP-93/57, CLNS-92/1176

References in corpus (11)

• Model-Building for Fractional Superstrings
• New Jacobi-Like Identities for Z_k Parafermion Characters
• Structure Constants of the Fractional Supersymmetry Chiral Algebras
• Central Charge Reduction and Spacetime Statistics in the Fractional Superstring
• Low-Lying States of the Six-Dimensional Fractional Superstring
• Heterotic Parafermionic Superstring
• Aspects of Fractional Superstrings
• The Worldsheet Conformal Field Theory of the Fractional Superstring
• Kac and New Determinants for Fractional Superconformal Algebras
• Tree scattering amplitudes of the spin-4/3 fractional superstring II: the twisted sectors
• Construction of the K=8 Fractional Superconformal Algebras

Cited by in corpus (3)

• Parafermionic polynomials, Selberg integrals and three-point correlation function in parafermionic Liouville field theory
• Fractional supersymmetric Liouville theory and the multi-cut matrix models
• Tree scattering amplitudes of the spin-4/3 fractional superstring II: the twisted sectors