The quantum mirror map of the D5 del Pezzo curve is expressed in D5 characters with a signed multi-covering structure, and it reproduces the effective chemical potentials of the (2,2) and (1,1,1,1) super Chern-Simons matrix models.
ABJM Matrix Model and 2D Toda Lattice Hierarchy
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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.
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Quantum Mirror Map for Del Pezzo Geometries
The quantum mirror map of the D5 del Pezzo curve is expressed in D5 characters with a signed multi-covering structure, and it reproduces the effective chemical potentials of the (2,2) and (1,1,1,1) super Chern-Simons matrix models.