2D FRACTIONAL SUPERSYMMETRY FOR RATIONAL CONFORMAL FIELD-THEORY - APPLICATION FOR 3RD-INTEGER SPIN STATES

A 2D fractional supersymmetry theory is algebraically constructed. The Lagrangian is derived using an adapted superspace including, in addit ion to a scalar field, two fields with spins 1/3, 2/3. This theory tur ns out to be a rational conformal field theory. The symmetry of this m odel goes beyond the super-Virasoro algebra and connects these third-i nteger spin states. Besides the stress-momentum tensor, we obtain a su percurrent of spin 4/3. Cubic relations are involved in order to close the algebra; the basic algebra is no longer a Lie or a super-lie alge bra. The central charge of this model is found to be 5/3. Finally, we analyze the form that a local invariant action should take.