NPAC Technical Report SCCS-269
Quantum Gravity, Random Geometry and Critical Phenomena
Mark Bowick, Enzo Marinari
Submitted March 01 1992
Abstract
We discuss
the theory of non-critical strings with extrinsic curvature embedded
in a target space dimension
d greater than one. We emphasize the analogy between
2d gravity coupled to matter and non self-avoiding liquid-like membranes
with bending rigidity.
We first outline the exact solution for strings in dimensions
d < 1 via the double scaling limit of matrix models
and then discuss the difficulties of an extension to d > 1 .
Evidence from recent and ongoing
numerical simulations of dynamically triangulated random surfaces
indicate that there is a non-trivial crossover from a crumpled
to an extended surface as the bending rigidity is increased.
If the cross-over is a true second order phase transition
corresponding to a critical point there is the exciting possibility of
obtaining a well defined continuum string theory for d > 1.