  We study both the classical and the quantum target space of (p,q) minimal
string theory, using the FZZT brane as a probe. By thinking of the target space
as the moduli space of FZZT branes, parametrized by the boundary cosmological
constant x, we see that classically it consists of a Riemann surface \CM_{p,q}
which is a p-sheeted cover of the complex x plane. However, we show using the
dual matrix model that the exact quantum FZZT observables exhibit Stokes'
phenomenon and are entire functions of x. Along the way we clarify some points
about the semiclassical limit of D-brane correlation functions. The upshot is
that nonperturbative effects modify the target space drastically, changing it
from \CM_{p,q} to the complex x plane. To illustrate these ideas, we study in
detail the example of (p,q)=(2,1), which is dual to the Gaussian matrix model.
Here we learn that the other sheets of the classical Riemann surface describe
instantons in the effective theory on the brane. Finally, we discuss possible
applications to black holes and the topological string.
