Stable Non--Perturbative Minimal Models Coupled to 2D Quantum Gravity

TL;DR

This paper generalizes stable solutions of string equations for 2D quantum gravity coupled to minimal models, revealing their relation to KdV hierarchies and providing numerical solutions for the Ising model.

Contribution

It extends non-perturbative stable solutions to general (p,q) minimal models coupled with 2D quantum gravity, linking them to generalized KdV flows and bi-hamiltonian structures.

Findings

Derived the most general string equations compatible with q-th KdV flows.

Established the relationship between these equations and bi-hamiltonian structures.

Provided a real non-singular numerical solution for the Ising model's string susceptibility.

Abstract

A generalisation of the non--perturbatively stable solutions of string equations which respect the KdV flows, obtained recently for the $(2m-1,2)$ conformal minimal models coupled to two--dimensional quantum gravity, is presented for the $(p,q)$ models. These string equations are the most general string equations compatible with the $q$--th generalised KdV flows. They exhibit a close relationship with the bi-hamiltonian structure in these hierarchies. The Ising model is studied as a particular example, for which a real non-singular numerical solution to the string susceptibility is presented.