Non-local conservation laws and flow equations for supersymmetric integrable hierarchies

TL;DR

This paper develops an extended set of flow equations for supersymmetric integrable hierarchies, revealing new symmetries and conserved quantities, with detailed analysis of specific affine superalgebra cases.

Contribution

It introduces an infinite series of Grassmann-odd and Grassmann-even flows that commute with existing hierarchies, expanding the understanding of supersymmetric integrable systems.

Findings

New non-local conserved quantities constructed

Extended symmetries including N=1 supersymmetry identified

Detailed example for affine superalgebras provided

Abstract

An infinite series of Grassmann-odd and Grassmann-even flow equations is defined for a class of supersymmetric integrable hierarchies associated with loop superalgebras. All these flows commute with the mutually commuting bosonic ones originally considered to define these hierarchies and, hence, provide extra fermionic and bosonic symmetries that include the built-in N=1 supersymmetry transformation. The corresponding non-local conserved quantities are also constructed. As an example, the particular case of the principal supersymmetric hierarchies associated with the affine superalgebras with a fermionic simple root system is discussed in detail.