### Abstract

We present a non-perturbative solution of large N matrix models modified by terms of the form g(Trø^{4})^{2}, which add microscopic wormholes to the random surface geometry. For g < g_{t} the sum over surfaces is in the same universality class as the g = 0 theory, and the string susceptibility exponent is reproduced by the conventional Liouville interaction ∼ e^{α+ø}. For g = g_{t} we find a different universality class, and the string susceptibility exponent agrees for any genus with Liouville theory where the interaction term is dressed by the other branch, e^{α-ø}. This allows us to define a double-scaling limit of the g = g_{t} theory. We also consider matrix models modified by terms of the form gO^{2}, where O is a scaling operator. A fine-tuning of g produces a change in this operator's gravitational dimension which is, again, in accord with the change in the branch of the Liouville dressing.

Original language | English (US) |
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Pages (from-to) | 264-282 |

Number of pages | 19 |

Journal | Nuclear Physics, Section B |

Volume | 434 |

Issue number | 1-2 |

DOIs | |

State | Published - Jan 23 1995 |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

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## Cite this

*Nuclear Physics, Section B*,

*434*(1-2), 264-282. https://doi.org/10.1016/0550-3213(94)00518-J