  We examine three--dimensional turbulent flows in the presence of solid-body
rotation and helical forcing in the framework of stochastic Schramm-L\"owner
evolution curves (SLE). The data stems from a run on a grid of $1536^3$ points,
with Reynolds and Rossby numbers of respectively 5100 and 0.06. We average the
parallel component of the vorticity in the direction parallel to that of
rotation, and examine the resulting $<\omega_\textrm{z}>_\textrm{z}$ field for
scaling properties of its zero-value contours. We find for the first time for
three-dimensional fluid turbulence evidence of nodal curves being conformal
invariant, belonging to a SLE class with associated Brownian diffusivity
$\kappa=3.6\pm 0.1$. SLE behavior is related to the self-similarity of the
direct cascade of energy to small scales in this flow, and to the partial
bi-dimensionalization of the flow because of rotation. We recover the value of
$\kappa$ with a heuristic argument and show that this value is consistent with
several non-trivial SLE predictions.
