Tree Scattering Amplitudes *

The spin-4/3 fractional superstring is characterized by a chiral algebra involving a spin-4/3 current on the world-sheet in addition to the energy-momentum tensor. These currents generate physical state conditions on the fractional superstring Fock space. Scattering amplitudes of these physical states are described which satisfy both spurious state decoupling and cyclic symmetry (duality). Examples of such amplitudes are calculated using an explicit c = 5 realization of the spin-4/3 current algebra. This representation has three flat coordinate boson fields and a global SO(2,1) Lorentz symmetry, permitting a particle interpretation of the amplitudes. String theories are characterized by the local symmetries of two-dimensional field theories on the string world-sheet. The bosonic string is invariant under diffeomorphisms and local Weyl rescalings on the world-sheet; whereas the superstring is characterized by a locally supersymmetric version of these symmetries. It is natural to ask whether other symmetries on the world-sheet can give rise to consistent string theories. Recently, a proposal for a large class of new string theories, called fractional superstrings, was advanced. Since fractional-spin fields exist in two-dimensional theories, one can imagine new local symmetries on the world-sheet involving fractional-spin currents (replacing the spin-3/2 supercurrent of the superstring). Evidence has been presented that fractional superstrings with spin 4/3, 6/5, and 10/9 currents on the world-sheet have potentially interesting phenomenologies in 6, 4 and 3 space-time dimensions, respectively. This talk will focus exclusively on the spin-4/3 fractional superstring and its tree scattering amplitudes. In the course of the discussion I will simply state many of the properties of the representation theory of the spin-4/3 current algebra on the string world-sheet; for proofs and more details, see Ref. 5. Classically, the spin-4/3 algebra is the constraint algebra arising from gauge-fixing the local worldsheet symmetry. Quantum mechanically, the constraints generate physical state conditions which pick out the propagating degrees of freedom from the larger string ∗ Talk presented at the 26th Erice workshop: “From Superstrings to Supergravity”. Visiting the Center for Theoretical Physics, M.I.T., Cambridge, MA 02139 until June 1993. E-mail address: [email protected].