On "Bosonic, Fermionic and Mixed" Supersymmetric 2-Dimensional Integrable Models

TL;DR

This paper demonstrates that supersymmetric integrable models in two dimensions can be linked to broad Poisson-bracket structures derived from superaffinizations of any bosonic or super-Lie algebra, expanding the class of such models.

Contribution

It generalizes the connection between supersymmetric integrable models and Poisson-bracket structures to include models based on any bosonic or super-Lie algebra, not just fermionic ones.

Findings

Supersymmetric models relate to superaffinizations of bosonic and super-Lie algebras.

The set of integrable models is expanded beyond purely fermionic algebra cases.

New classes of supersymmetric integrable models are identified.

Abstract

It is shown that supersymmetric integrable models in two dimensions, both relativistic (i.e. super-Toda type theories) and non-relativistic (reductions of super-KP hierarchies) can be associated to general Poisson-brackets structures given by superaffinizations of any bosonic Lie or any super-Lie algebra. This result allows enlarging the set of supersymmetric integrable models, which are no longer restricted to the subclass of superaffinizations of purely fermionic super-Lie algebras (that is admitting fermionic simple roots only).