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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 multicritical unitary matrix models map to non-singular solutions of the 'renormalization group' equation for the string susceptibility, [Formula: see text]. 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 [Formula: see text].
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Dalley et al. (1992) studied this question.
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