ZZ brane amplitudes from matrix models

Abstract

We study instanton contribution to the partition function of the one matrix model in the k-th multicritical region, which corresponds to the (2,2k-1) minimal model coupled to Liouville theory. The instantons in the one matrix model are given by local extrema of the effective potential for a matrix eigenvalue and identified with the ZZ branes in Liouville theory. We show that the 2-instanton contribution in the partition function is universal as well as the 1-instanton contribution and that the connected part of the 2-instanton contribution reproduces the annulus amplitudes between the ZZ branes in Liouville theory. Our result serves as another nontrivial check on the correspondence between the instantons in the one matrix model and the ZZ branes in Liouville theory, and also suggests that the expansion of the partition function in terms of the instanton numbers are universal and gives systematically ZZ brane amplitudes in Liouville theory.

29 pages, 4 figures; v2:how to scale x is generalized; v3:introduction and the last section are revised, typos corrected

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• Strings from Tachyons
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• Stokes Phenomena and Quantum Integrability in Non-critical String/M Theory
• T-duality of ZZ-brane
• Macroscopic loop amplitudes in the multi-cut two-matrix models
• c=1 from c<1: Bulk and boundary correlators
• Resurgence of one-point functions in a matrix model for 2D type IIA superstrings