Matrix Model and Stationary Problem in Toda Chain
arXiv:hep-th/0507071 · doi:10.1007/s11232-006-0001-0
Abstract
We analyze the stationary problem for the Toda chain, and show that arising geometric data exactly correspond to the multi-support solutions of one-matrix model with a polynomial potential. For the first nontrivial examples the Hamiltonians and symplectic forms are calculated explicitly, and the consistency checks are performed. The corresponding quantum problem is formulated and some its properties and perspectives are discussed.
11 pages, LaTeX; Based on talks at "Classical and quantum integrable systems", Dubna, January 2005 and "Selected topics of modern mathematical physics", St.Petersburg, June 2005, and a lecture for the minicourse: "Toda lattices: basics and perspectives", Fields Institute, Toronto, April 2005
References in corpus (8)
- A Perturbative Window into Non-Perturbative Physics
- Small Instantons, Little Strings and Free Fermions
- N=1 and N=2 Geometry from Fluxes
- Seiberg-Witten Theory and Random Partitions
- Seiberg-Witten prepotential from instanton counting
- Whitham Prepotential and Superpotential
- Factorization of Seiberg-Witten Curves and Compactification to Three Dimensions
- Critical Points of Glueball Superpotentials and Equilibria of Integrable Systems