Watersheds are Schramm-Loewner Evolution curves

TL;DR

This paper demonstrates that in the continuum limit, watersheds dividing drainage basins are described by Schramm-Loewner Evolution curves with a specific parameter, indicating conformal invariance and a connection to logarithmic CFT.

Contribution

It provides the first physical example of an SLE curve with <2, challenging existing duality conjectures and suggesting a new link between watersheds and conformal field theories.

Findings

Watersheds are described by SLE with =1.734

Results support conformal invariance in random landscapes

Indicates watersheds may correspond to a logarithmic CFT with ca0/2

Abstract

We show that in the continuum limit watersheds dividing drainage basins are Schramm-Loewner Evolution (SLE) curves, being described by one single parameter $\kappa$. Several numerical evaluations are applied to ascertain this. All calculations are consistent with SLE$_\kappa$, with $\kappa=1.734\pm0.005$, being the only known physical example of an SLE with $\kappa<2$. This lies outside the well-known duality conjecture, bringing up new questions regarding the existence and reversibility of dual models. Furthermore it constitutes a strong indication for conformal invariance in random landscapes and suggests that watersheds likely correspond to a logarithmic Conformal Field Theory (CFT) with central charge $c\approx-7/2$.