We obtain the bi-Hamiltonian structure of the super KP hierarchy based on the even super KP operator $\Lambda = \theta^{ 2} + \sum^{ \infty}_{ i=-2}U_{ i} \theta^{ -i-1}$, as a supersymmetric extension of the ordinary KP bi-Hamiltonian structure. It is expected to give rise to a universal super $W$-algebra incorporating all known extended superconformal $W_{ N}$ algebras by reduction. We also construct the super BKP hierarchy by imposing a set of anti-self-dual constraints on the super KP hierarchy.
Categories: hep-th