  We investigate 2D topological gravity theories with matter fields turned on.
We compute correlators of boundary creation operators with extra matter
insertions. We provide a systematic procedure to determine a set of
$\alpha$-states on which the correlation functions of the different boundary
operators factorize. Our results suggest that the boundary dual is an ensemble
average of theories with different numbers of replicas of a seed matter
contribution that is represented by excitations on top of the gravity sector.
The construction of the $\alpha$-states and the subsequent computations in the
Hilbert space point of view are most conveniently done when the bulk couplings
of the matter fields are expanded in a basis of vortices, which can be thought
of as a 1-dimensional analogue of the SD-branes. We further demonstrate the
existence of null states and the conditions imposed by reflection positivity.
Moreover, in the CGS model with only disk and cylinder topologies, we map the
baby universe creation and annihilation operators to the coupling constants in
the one time SYK model, which allows us to match the wormhole and half-wormhole
contributions in the CGS model explicitly to those identified in the SYK model.
This explicitly realizes Coleman's initial idea. Some details of the
computations in a variety of concrete models are presented.
