## Abstract

We generalize the Marinari-Parisi definition for pure two-dimensional quantum gravity (k=2) to all non-unitary minimal multicritical points (k≥3). The resulting interacting Fermi gas theory is treated in the collective field framework. Making use of the fact that the matrices evolve in Langevin time, the jacobian from matrix coordinates to collective modes is similar to the corresponding jacobian in d=1 matrix models. The collective field theory is analyzed in the planar limit. The saddle point eigenvalue distribution is the one that defines the original multicritical point and therefore exhibits the appropriate scaling behaviour. Some comments on the non-perturbative properties of the collective field theory as well as comments on the Virasoro constraints associated with the loop equations are made at the end of this letter. There we also make some remarks on the fermionic formulation of the model and its integrability, as a non-local version of the non-linear Schrödinger model.

Original language | English |
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Pages (from-to) | 225-232 |

Number of pages | 8 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 281 |

Issue number | 3-4 |

DOIs | |

State | Published - 14 May 1992 |

Externally published | Yes |

### Bibliographical note

Funding Information:Supported in part by the Fund for Basic Research administered by the Israel Academy of Sciences and Humanities and by the Fonds zur F/~rderung der wissenschaflicher Forschung, Austria, Project Nr. P8485-TEC. E-mailaddress: [email protected]. l.e. matrix defined over a zero-dimensional space-time. We will refer to them as zero-dimensional models. The stabilized models, in which matrices depend upon the Langevin time co-ordinate will be referred to as the one-dimensional models. One should not, of course, mix this terminology with "dimension" counting in target space, i.e., values of the central charge of matter coupled to gravity.

## ASJC Scopus subject areas

- Nuclear and High Energy Physics