  The kinematic dynamo (KD) describes the growth of magnetic fields generated
by the flow of a conducting medium in the limit of vanishing backaction of the
fields onto the flow. The KD is therefore an important model system for
understanding astrophysical magnetism. Here, the mathematical correspondence
between the KD and a specific stochastic differential equation (SDE) viewed
from the perspective of the supersymmetric theory of stochastics (STS) is
discussed. The STS is a novel, approximation-free framework to investigate
SDEs. The correspondence reported here permits insights from the STS to be
applied to the theory of KD and vice versa. It was previously known that the
fast KD in the idealistic limit of no magnetic diffusion requires chaotic
flows. The KD-STS correspondence shows that this is also true for the diffusive
KD. From the STS perspective, the KD possesses a topological supersymmetry and
the dynamo effect can be viewed as its spontaneous breakdown. This
supersymmetry breaking can be regarded as the stochastic generalization of the
concept of dynamical chaos. As this supersymmetry breaking happens in both the
diffusive and the non-diffusive case, the necessity of the underlying SDE being
chaotic is given in either case. The observed exponentially growing and
oscillating KD modes prove physically that dynamical spectra of the STS
evolution operator that break the topological supersymmetry exist with both,
real and complex ground state eigenvalues. Finally, we comment on the
non-existence of dynamos for scalar quantities.
