ABSTRACT
A breakthrough understanding of the theoretical essence of stochastic chaos came from the theory of supersymmetric field theories. The easiest way to understand the unconditional presence of this supersymmetry is to recall that temporal evolution is the stochastically averaged pullback and that any pullback commutes with the exterior derivative. The commutativity of an operator with the evolution operator says that this operator is a symmetry of the model. Supersymmetries, however, are very hard to break pertubratively because of what is generally known as non-renormalization theorems. The most important or qualitative part of the dynamics in models with spontaneously broken global symmetry occupies a reduced phase space and/or in a reduced number of “low-energy” variables and the low-energy effective theories are the theories describing this dynamics. The order parameter must be a gapless fermionic field consisting of supersymmetric partners of these unstable variables.
