Matrix Models of Two-Dimensional Gravity and Discrete Toda Theory
Abstract
Recursion relations for orthogonal polynomials, arising in the study of one-matrix model of two-dimensional gravity, are shown to be equivalent 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.
- Publication:
-
Modern Physics Letters A
- Pub Date:
- 1996
- DOI:
- 10.1142/S0217732396001788
- arXiv:
- arXiv:hep-th/9605175
- Bibcode:
- 1996MPLA...11.1797H
- Keywords:
-
- High Energy Physics - Theory
- E-Print:
- 10 pages, Latex file