2D Fractional Supersymmetry for Rational Conformal Field Theory. Application for Third-Integer Spin States

Abstract

A 2D- fractional supersymmetry theory is algebraically constructed. The Lagrangian is derived using an adapted superspace including, in addition to a scalar field, two fields with spins 1/3,2/3. This theory turns out to be a rational conformal field theory. The symmetry of this model goes beyond the super Virasoro algebra and connects these third-integer spin states. Besides the stress-momentum tensor, we obtain a supercurrent 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 algebra. The central charge of this model is found to be 5/3. Finally, we analyse the form that a local invariant action should take.

LaTex, 20 pages. Revised in response to referees' Comments

References in corpus (2)

• Group Theoretical Foundations of Fractional Supersymmetry
• Local Fractional Supersymmetry for Alternative Statistics

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