  We study the effect of ZZ instantons in c = 1 string theory, and demonstrate
that they give rise to non-perturbative corrections to scattering amplitudes
that do not saturate unitarity within the closed string sector. Beyond the
leading non-perturbative order, logarithmic divergences are canceled between
worldsheet diagrams of different topologies, due to the
Fischler-Susskind-Polchinski mechanism. We propose that the closed string
vacuum in c = 1 string theory is non-perturbatively dual to a state of the
matrix quantum mechanics in which all scattering states up to a given energy
with no incoming flux from the "other side" of the potential are occupied by
free fermions. Under such a proposal, we find detailed agreement of
non-perturbative corrections to closed string amplitudes in the worldsheet
description and in the dual matrix model.
