  We study a generalization of the Langevin equation, that describes
fluctuations, of commuting degrees of freedom, for scalar field theories with
worldvolumes of arbitrary dimension, following Parisi and Sourlas and
correspondingly generalizes the Nicolai map. Supersymmetry appears inevitably,
as defining the consistent closure of system+fluctuations and it can be probed
by the identities satisfied by the correlation functions of the noise fields,
sampled by the action of the commuting fields. This can be done effectively,
through numerical simulations.
  We focus on the case where the target space is invariant under global
rotations, in Euclidian signature, corresponding to global Lorentz
transformations, in Lorentzian signature. This can describe target space
supersymmetry.
  In this case a cross--term, that is a total derivative for abelian
isometries, or when the fields are holomorphic functions of their arguments,
can lead to obstructions. We study its effects and find that, in two
dimensions, it cannot lead to the appearance of the holomorphic anomaly, in any
event, when fluctuations are taken into account, because continuous symmetries
can't be broken in two dimensions.
