2D fractional supersymmetry and conformal field theory for alternative statistics

  title={2D fractional supersymmetry and conformal field theory for alternative statistics},
  author={Michel Rausch de Traubenberg and Pascal Simon},
  journal={Nuclear Physics},

Fractional Supersymmetry and F − fold Lie

It is generally held that supersymmetry is the only non-trivial extension of the Poincaré algebra. This point of view is based on the two theorems [1, 2]. However, as usual, if some of the

Fractional supersymmetry and Fth-roots of representations

A generalization of super-Lie algebras is presented. It is then shown that all known examples of fractional supersymmetry can be understood in this formulation. However, the incorporation of

Some Results on Cubic and Higher Order Extensions of the Poincare Algebra

In these lectures we study some possible higher order (of degree greater than two) extensions of the Poincare algebra. We first give some general properties of Lie superalgebras with some emphasis on

On Supersymmetric Quantum Mechanics

This paper constitutes a review on N = 2 fractional supersym-metric Quantum Mechanics of order k. The presentation is based on the introduction of a generalized Weyl-Heisenberg algebra W k . It is

Fractional supersymmetry and hierarchy of shape invariant potentials

Fractional supersymmetric quantum mechanics is developed from a generalized Weyl-Heisenberg algebra. The Hamiltonian and the supercharges of fractional supersymmetric dynamical systems are built in

A parafermionic generalization of the Jaynes–Cummings model

We introduce a parafermionic version of the Jaynes–Cummings Hamiltonian, by coupling k Fock parafermions (nilpotent of order F) to a 1D harmonic oscillator, representing the interaction with a single

Two dimensional fractional supersymmetric conformal field theories and the two point functions

A general two-dimensional fractional supersymmetric conformal field theory is investigated. The structure of the symmetries of the theory is studied. Then, applying the generators of the closed

Parafermions for higher order extensions of the Poincaré algebra and their associated superspace

Parafermions of orders 2 and 3 are shown to be the fundamental tool to construct superspaces related to cubic and quartic extensions of the Poincaré algebra. The corresponding superfields are

Deformations, Contractions and Classification of Lie Algebras of Order 3

Lie algebras of order F (or F −Lie algebras) are possible generalisations of Lie algebras (F = 1) and Lie superalgebras (F = 2). These structures have been used to implement new non-trivial



Geometrical Foundations of Fractional Supersymmetry

A deformed q-calculus is developed on the basis of an algebraic structure involving graded brackets. A number operator and left and right shift operators are constructed for this algebra, and the

Group theoretical foundations of fractional supersymmetry

Fractional supersymmetry denotes a generalization of supersymmetry which may be constructed using a single real generalized Grassmann variable, θ=θ,θn=0, for arbitrary integer n=2,3,.... An explicit

Local Fractional Supersymmetry for Alternative Statistics

A group theory justification of one-dimensional fractional supersymmetry is proposed using an analog of a coset space, just like the one introduced in 1-D supersymmetry. This theory is then gauged to

Infinite additional symmetries in two-dimensional conformal quantum field theory

This paper investigates additional symmetries in two-dimensional conformal field theory generated by spin s = 1/2, 1,...,3 currents. For spins s = 5/2 and s = 3, the generators of the symmetry form