Matrix Models of TwoDimensional Gravity and Discrete Toda Theory
Abstract
Recursion relations for orthogonal polynomials, arising in the study of onematrix model of twodimensional gravity, are shown to be equivalent to the equations of the Todachain 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:hepth/9605175
 Bibcode:
 1996MPLA...11.1797H
 Keywords:

 High Energy Physics  Theory
 EPrint:
 10 pages, Latex file