ABJM Matrix Model and 2D Toda Lattice Hierarchy

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.

35 pages, 7 eps figures; v2: references added

References in corpus (10)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Fractional M2-branes
• Summing Up All Genus Free Energy of ABJM Matrix Model
• Exact results on ABJ theory and the refined topological string
• Exact ABJM Partition Function from TBA
• Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
• Exact Instanton Expansion of Superconformal Chern-Simons Theories from Topological Strings
• Operators and higher genus mirror curves
• Superconformal Chern-Simons Theories from del Pezzo Geometries
• Dualities in ABJM Matrix Model from Closed String Viewpoint