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It was known that one-point functions in the ABJM matrix model (obtained byapplying the localization technique to one-point functions of the half-BPSWilson loop operator in the ABJM theory) satisfy the Jacobi-Trudi formula,which strongly indicates the integrable structure of the system. In this paper,we identify the integrable structure of two-point functions in the ABJM matrixmodel as the two-dimensional Toda lattice hierarchy. The identification impliesinfinitely many non-linear differential equations for the generating functionof the two-point functions.

ABJM Matrix Model and 2D Toda Lattice Hierarchy