The super KP origin of the super W 1+∞ algebra and its topological version

Abstract

The integrable KP hierarchy via its hamiltonian structures is known to incorporate all known extended conformal W-algebras. In this paper, we discuss the appropriate supersymmetric generalization of it. We obtain the (first) hamiltonian structure of super KP hierarchy based on the even super KP operator Λ = θ 2 + Σ i = 0 ∞ U i θ − i−1 . It naturally generates a super W 1+∞ algebra whose bosonic sector is identified with W 1+∞⊗ W 1+∞. We show that a subalgebra of it turns out to be isomorphic to the known N = 2 super W ∞ algebra without center. Moreover, we find that a twisted version of super W 1+∞ gives rise to a topological-anti-topological W 1+∞ algebra containing simultaneously two BRST operators. Our results not only provide a promising framework of studying 2d quantum supergravity and non-critical superstrings, but also open a channel towards constructing more interesting topological field theories.