ZZ brane amplitudes from matrix models

We study instanton contribution to the partition function of the one matrixmodel in the k-th multicritical region, which corresponds to the (2,2k-1)minimal model coupled to Liouville theory. The instantons in the one matrixmodel are given by local extrema of the effective potential for a matrixeigenvalue and identified with the ZZ branes in Liouville theory. We show thatthe 2-instanton contribution in the partition function is universal as well asthe 1-instanton contribution and that the connected part of the 2-instantoncontribution reproduces the annulus amplitudes between the ZZ branes inLiouville theory. Our result serves as another nontrivial check on thecorrespondence between the instantons in the one matrix model and the ZZ branesin Liouville theory, and also suggests that the expansion of the partitionfunction in terms of the instanton numbers are universal and givessystematically ZZ brane amplitudes in Liouville theory.Comment: 29 pages, 4 figures; v2:how to scale x is generalized; v3:introduction and the last section are revised, typos correcte