String field theory in minimal model backgrounds and nonperturbative two-dimensional gravity

Abstract

The classical phase space of free closed-string field theory in the background of (p, q) minimal models is studied. It is shown that in the limit q → ∞ for fixed p, this becomes the phase space of p - 1 massless chiral bosons on a two-dimensional target space, twisted by Z_p. It is argued that in the interacting theory, the bosons remain free and massless in the limit, but the non-linear gauge symmetries of string field theory require the imposition of W_p-algebra conditions on the Hilbert space, allowing a single physical state. The wave function for this state is the KdV τ-function associated to non-perturbative two-dimensional gravity in the matrix-model approach.