## 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 2 d 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.

Original language | English (US) |
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Pages (from-to) | 1209-1221 |

Number of pages | 13 |

Journal | General Relativity and Gravitation |

Volume | 24 |

Issue number | 12 |

DOIs | |

State | Published - Dec 1 1992 |

## ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)