## Abstract

We introduce conformal multi-matrix models (CMMs) as an alternative to conventional multi-matrix model description of two-dimensional gravity interacting with c < 1 matter. We define CMMs as solutions to (discrete) extended Virasoro constraints. We argue that the so defined alternatives of multi-matrix models represent the same universality classes in the continuum limit, while at the discrete level they provide explicit solutions to the multi-component KP-hierarchy and by definition satisfy the discrete W-constraints. We prove that discrete CMMs coincide with the (p, q)-series of 2d gravity models in a well-defined continuum limit, thus demonstrating that they provided a proper generalization of the hermitian one-matrix model.

Original language | English |
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Pages (from-to) | 717-750 |

Number of pages | 34 |

Journal | Nuclear Physics B |

Volume | 404 |

Issue number | 3 |

DOIs | |

Publication status | Published - 6 Sep 1993 |

Externally published | Yes |