  Type 0A string theory in the (2,4k) superconformal minimal model backgrounds
and the bosonic string in the (2,2k-1) conformal minimal models, while
perturbatively identical in some regimes, may be distinguished
non-perturbatively using double scaled matrix models. The resolvent of an
associated Schrodinger operator plays three very important interconnected
roles, which we explore perturbatively and non-perturbatively. On one hand, it
acts as a source for placing D-branes and fluxes into the background, while on
the other, it acts as a probe of the background, its first integral yielding
the effective force on a scaled eigenvalue. We study this probe at disc, torus
and annulus order in perturbation theory, in order to characterize the effects
of D-branes and fluxes on the matrix eigenvalues. On a third hand, the
integrated resolvent forms a representation of a twisted boson in an associated
conformal field theory. The entire content of the closed string theory can be
expressed in terms of Virasoro constraints on the partition function, which is
realized as wavefunction in a coherent state of the boson. Remarkably, the
D-brane or flux background is simply prepared by acting with a vertex operator
of the twisted boson. This generates a number of sharp examples of open-closed
duality, both old and new. We discuss whether the twisted boson conformal field
theory can usefully be thought of as another holographic dual of the
non-critical string theory.
