Relation between reducible Lagrangian varieties and open topological strings

Determine the precise relation between the reducible Lagrangian varieties obtained from the three q-deformed matrix models and the geometry underlying open topological strings.

Background

The paper interprets inverse-characteristic-polynomial correlators in the Chern–Simons, q-Laguerre, and q-Gaussian matrix models as quantizations of Lagrangian varieties. Although this construction is suggestive of open topological-string geometry, the authors explicitly state that the two constructions are not identical and that their precise relationship has not been established.

References

This picture is suggestive of the geometry underlying open topological strings, although the two constructions are not identical and the precise relation between them remains to be understood.

— Lagrangian varieties from $q$-matrix models  (2609.01454 - Mishnyakov et al., 1 Sep 2026) in Abstract; Introduction, Section 1

At the moment we do not know how to realize the curve qG-ellipric in the matrix model.

qG-ellipric:

1−T=y2(1−a1T)(1−a2T) ,1- T = y^2 (1-a_1T) (1-a_2 T)~,

— Lagrangian varieties from $q$-matrix models  (2609.01454 - Mishnyakov et al., 1 Sep 2026) in Section q-Gaussian matrix model, subsection Classical curve