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arXiv · hep-th/9603149

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

A. Perez·M. Rausch de Traubenberg·P. Simon
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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.

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A. Perez, M. Rausch de Traubenberg, P. Simon. 1997-01-29. 2D Fractional Supersymmetry for Rational Conformal Field Theory. Application for Third-Integer Spin States. https://doi.org/10.1016/s0550-3213(96)00522-6

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