Quantum gravity, random geometry and critical phenomena

Details Quantum gravity, random geometry and critical phenomena Quantum gravity, random geometry and critical phenomena

Dec 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992gregr..24.1209b&link_type=abstract

General Relativity and Gravitation, Volume 24, Issue 12, pp.1209-1221

Physics

Scientific paper

We discuss the theory of non-critical strings with extrinsic curvature embedded in a target space dimensiond 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 dimensionsd<1 via the double scaling limit of matrix models and then discuss the difficulties of an extension tod>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 ford>1.

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