THE SUPER KP ORIGIN OF THE SUPER W(1+INFINITY) ALGEBRA AND ITS TOPOLOGICAL VERSION

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 LAMBDA = theta-2 + SIGMA(i)infinity = 0U(i)theta(-i-1). It naturally generates a super W1 + infinity algebra whose bosonic sector is identified with W1 + infinity x W1 + infinity. We show that a subalgebra of it turns out to be isomorphic to the known N = 2 super W(infinity) algebra without center. Moreover, we find that a twisted version of super W1 + infinity gives rise to a topological-anti-topological W1 + infinity 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.