Determinant formulas for matrix model free energy
D. Vasiliev
A. I. Alikhanov Institute for Theoretical and Experimental Physics, 117218 Moscow, Russia
Moscow Institute of Physics and Technology, 117303 Moscow, Russia
PACS: 11.15.Pg, 11.15.Tk
Abstract
The paper contains a new non-perturbative representation for
subleading contribution to the free energy of multicut solution for hermitian
matrix model. This representation is a generalisation of the formula,
proposed by Klemm, Marino and Theisen for two cut solution, which was
obtained by comparing the cubic matrix model with the topological B-model on
the local Calabi-Yau geometry and was checked perturbatively.
In this paper we give a direct proof of their formula and generalise it to
the general multicut solution.