  A connection between non-perturbative formulations of quantum gravity and
perturbative string theory is exhibited, based on a formulation of the
non-perturbative dynamics due to Markopoulou. In this formulation the dynamics
of spin network states and their generalizations is described in terms of
histories which have discrete analogues of the causal structure and many
fingered time of Lorentzian spacetimes. Perturbations of these histories turn
out to be described in terms of spin systems defined on 2-dimensional timelike
surfaces embedded in the discrete spacetime. When the history has a classical
limit which is Minkowski spacetime, the action of the perturbation theory is
given to leading order by the spacetime area of the surface, as in bosonic
string theory. This map between a non-perturbative formulation of quantum
gravity and a 1+1 dimensional theory generalizes to a large class of theories
in which the group SU(2) is extended to any quantum group or supergroup. It is
argued that a necessary condition for the non-perturbative theory to have a
good classical limit is that the resulting 1+1 dimensional theory defines a
consistent and stable perturbative string theory.
