Relate directed LQG metrics to the directed landscape in the zero-gamma limit

Determine whether the directed LQG metrics converge, after appropriate centering and rescaling and with suitable behavior of theta, to the directed landscape as gamma tends to zero.

Background

The authors expect directed LQG metrics to have deterministic limits as gamma tends to zero, but propose studying their second-order fluctuations. The directed landscape is the canonical scaling limit in integrable directed last-passage percolation, making convergence from directed LQG a concrete unresolved question.

References

Do the directed LQG metrics of Conjecture~\ref{conj-directed} converge, in some sense, to the directed landscape when we send $\gamma\to 0$ (with some appropriate behavior for $\theta$) and re-center and re-scale appropriately?

— Directed distances in bipolar-oriented triangulations: exact exponents and scaling limits  (2510.26123 - Borga et al., 30 Oct 2025) in Problem 2, Section 3, Parallels with directed first- and last-passage percolation