## Abstract

We present the partition function of the Generalized Kontsevich Model (GKM) in the form of a Toda lattice τ-function and discuss various implications of non-vanishing "negative-time" and "zero-time" variables: they appear to modify the original GKM action by negative-power and logarithmic contributions, respectively. It is shown that such a deformed τ-function satisfies the same string equation as the original one. In the case of quardratic potentials GKM turns out to describe forced Toda chain hierarchy and thus corresponds to a discrete matrix model, with the role of matrix size played by the zero-time (at integer positive points). This relation allows one to discuss the double-scaling continuum limit entirely in terms of GKM, i.e. essentially in terms of finite-fold integrals.

Original language | English |
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Pages (from-to) | 339-378 |

Number of pages | 40 |

Journal | Nuclear Physics B |

Volume | 397 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 24 May 1993 |

Externally published | Yes |