  We study material lines and passive vectors in a model of turbulent flow at
infinite-Reynolds number, the Kraichnan-Kazantsev ensemble of velocities that
are white-noise in time and rough (Hoelder continuous) in space. It is argued
that the phenomenon of ``spontaneous stochasticity'' generalizes to material
lines and that conservation of circulations generalizes to a ``martingale
property'' of the stochastic process of lines.
