In the context of field theory Ward identities are functional
identites generated by internal symmmetries of the model. They
generally appear as relations between Feynman diagrams, allowing to
simplify the perturbative expansion, and in some cases even to close
the Schwinger-Dyson equation. A natural question is whether
symmetry-generated identities may also help to study models where
standard renormalization group techniques do not apply. In this
context, in collaboration with M. Zirnbauer and T. Spencer, we
considered a nonlinear sigma model, which is the key ingredient in
the construction and study of certain stochastic processes with
memory. The corresponding integral is invariant under supersymmetric
transformations that generate an infinite family of Ward identities.
Though these identities have no interpretation as Feynman diagrams,
they proved to be a key ingredient in the analysis of the model.