# ABJM Matrix Model and 2D Toda Lattice Hierarchy

## TL;DR

This paper reveals that the two-point functions in the ABJM matrix model are governed by the two-dimensional Toda lattice hierarchy, indicating an underlying integrable structure with many nonlinear differential equations.

## Contribution

It identifies the integrable structure of two-point functions in the ABJM matrix model as the 2D Toda lattice hierarchy, extending previous knowledge from one-point functions.

## Key findings

- Two-point functions satisfy the 2D Toda lattice hierarchy.
- The generating function obeys infinitely many nonlinear differential equations.
- The integrable structure suggests deep mathematical properties of the ABJM matrix model.

## Abstract

It was known that one-point functions in the ABJM matrix model (obtained by applying the localization technique to one-point functions of the half-BPS Wilson 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 matrix model as the two-dimensional Toda lattice hierarchy. The identification implies infinitely many non-linear differential equations for the generating function of the two-point functions.