Supersymmetric BKP systems and their symmetries

TL;DR

This paper constructs and analyzes the symmetries of supersymmetric BKP hierarchies, revealing their algebraic structures and introducing a new constrained hierarchy with supersymmetric Block type symmetry.

Contribution

It introduces the additional symmetries of the supersymmetric BKP hierarchy, generalizes to a two-component hierarchy, and defines a new constrained system with supersymmetric Block symmetry.

Findings

Additional symmetries form a B type $SW_{1+ abla}$ Lie algebra.

Generalization to a supersymmetric two-component BKP hierarchy.

Definition of a new supersymmetric Drinfeld-Sokolov hierarchy of type D.

Abstract

In this paper, we construct the additional symmetries of the supersymmetric BKP(SBKP) hierarchy. These additional flows constitute a B type $SW_{1+\infty}$ Lie algebra because of the B type reduction of the supersymmetric BKP hierarchy. Further we generalize the SBKP hierarchy to a supersymmetric two-component BKP (S2BKP) hierarchy equipped with a B type $SW_{1+\infty}\bigoplus SW_{1+\infty}$ Lie algebra. As a Bosonic reduction of the S2BKP hierarchy, we define a new constrained system called the supersymmetric Drinfeld-Sokolov hierarchy of type D which admits a $N=2$ supersymmetric Block type symmetry.