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arXiv · hep-th/9605175

Matrix Models of Two-dimensional Gravity and Discrete Toda Theory

Masato Hisakado·Miki Wadati
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Abstract

Recursion relations for orthogonal polynominals, arising in the study of the one-matrix model of two-dimensional gravity, are shown to be equvalent to the equations of the Toda-chain hierarchy supplemented by additional Virasoro constraints. This is the case without the double scaling limit. A discrete time variable to the matrix model is introduced. The discrete time dependent partition functions are given by $τ$ functions which satisfy the discrete Toda molecule equation. Further the relations between the matrix model and the discrete time Toda theory are discussed.

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Masato Hisakado, Miki Wadati. 1996-05-23. Matrix Models of Two-dimensional Gravity and Discrete Toda Theory. https://doi.org/10.1142/s0217732396001788

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