Quantum gravity,random geometry and critical phenomena |
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Authors: | Mark J. Bowick Enzo Marinari |
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Affiliation: | (1) Physics Department, Syracuse University, 13244-1130 Syracuse, New York, USA;(2) Present address: Dipartimento di Fisica and INFN, Universita di Roma Tor Vergata, Viale della Ricerca Scientifica, I-00173 Roma, Italy |
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Abstract: | 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. This essay received the third award from the Gravity Research Foundation, 1992-Ed. |
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