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

TL;DR

This paper constructs a 2D fractional supersymmetry theory involving fields with spins 1/3 and 2/3, resulting in a rational conformal field theory with novel algebraic structures and third-integer spin states.

Contribution

It introduces an algebraic framework for 2D fractional supersymmetry with new algebraic relations and constructs a rational conformal field theory incorporating third-integer spin states.

Findings

The theory has a central charge of 5/3.

A supercurrent of spin 4/3 is derived.

The algebra involves cubic relations beyond Lie or super-Lie structures.

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.