Matrix Models of Two-dimensional Gravity and Discrete Toda Theory

Details Matrix Models of Two-dimensional Gravity and Discrete Toda Theory Matrix Models of Two-dimensional Gravity and Discrete Toda Theory

1996-05-23

arxiv.org/abs/hep-th/9605175v1

Mod.Phys.Lett. A11 (1996) 1797-1806

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, Latex file

Scientific paper

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 $\tau$ 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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