Octonionic Supersymmetry

A two-dimensional, relativistic, superconformal, integrable model obtaining from the super WZNW model through a hamiltonian reduction procedure, which prescribes putting equal to non-zero constant those supercurrents corresponding to the positive or negative simple roots of the WZNW superalgebra.

The standard construction [1] requires a superalgebra admitting a presentation in terms of fermionic simple roots only (this condition can however be relaxed [2]). The super Lie algebra-valued supercurrents ψ, of the super WZNW model must be understood as super-Cartan forms

where D, are supersymmetric derivatives. The number of independent superfields in a super Toda model equals the rank r of the associated superalgebra. The simplest example of a super Toda model is the superLiouville theory, associated to the rank 1 superalgebra . The equation satisfied by the single bosonic superfield Φ is

Super Toda modelsadmit a...