Unitary Matrix Models and 2D Quantum Gravity (Virasoro constraints modified)

الأصل · EN

The KdV and modified KdV integrable hierarchies are shown to be different descriptions of the same 2D gravitational system -- open-closed string theory. Non-perturbative solutions of the multi-critical unitary matrix models map to non-singular solutions of the `renormalisation group' equation for the string susceptibility, [P,Q]=Q. We also demonstrate that the large N solutions of unitary matrix integrals in external fields, studied by Gross and Newman, equal the non-singular pure closed-string solutions of [P,Q]=Q.