On the Supersymmetric BKP-Hierarchy

TL;DR

This paper establishes the Hamiltonian structure of the supersymmetric BKP hierarchy using a nonlinear super-Virasoro algebra extension and explores its relation to other integrable hierarchies.

Contribution

It proves the SBKP hierarchy is Hamiltonian with respect to a specific super-Virasoro algebra extension and links it to other SKdV-type hierarchies.

Findings

SBKP hierarchy is Hamiltonian with a nonlinear super-Virasoro algebra

Extension of SBKP hierarchy by odd flows compatible with Hamiltonian structure

Equivalence of extended hierarchy to Manin-Radul SBKP hierarchy

Abstract

We prove that the supersymmetric BKP-hierarchy of Yu (SBKP_2) is hamiltonian with respect to a nonlinear extension of the N=1 Super-Virasoro algebra (W_SBKP) by fields of spin k, where k>3/2 and 2k = 0,3 mod 4. Moreover, we show how to associate in a similar manner an N=1 W-superalgebra with every integrable hierarchy of the SKdV-type. We also show using dressing transformations how to extend, in a way which is compatible with the hamiltonian structure, the SBKP_2-hierarchy by odd flows, as well as the equivalence of this extended hierarchy to the SBKP-hierarchy of Manin-Radul.