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

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

1992-06-15

arxiv.org/abs/hep-th/9206060v2

Mod.Phys.Lett. A7 (1992) 2753-2762

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, PUPT-1325

Scientific paper

10.1142/S0217732392002226

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, $[\tilde{P},Q]=Q$. 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 $[\tilde{P},Q]=Q$.

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