Determinant formulas for matrix model free energy

The paper contains a new nonperturbative representation for the subleading contribution to the free energy of a multicut solution for a Hermitian matrix model. This representation is a generalization of the formula proposed by Klemm, Marino, and Theisen for a two-cut solution, which was obtained by comparing the cubic matrix model with the topological B-model on the local Calabi-Yau geometry \(\widehat{II}\) and was checked perturbatively. In this paper, I give a direct proof of their formula and generalize it to the general multicut solution.