Disordered QFTs and Parisi-Sourlas supersymmetry

I will discuss the critical physics of a class of disordered
(impure) quantum field theories, called random field models. It was
conjectured by Parisi and Sourlas 40 years ago that these models have a
critical point characterized by an emergent supersymmetry and an
interesting 'dimensional reduction' property - that says they are related
to a lower dimensional pure critical point (i.e. an ordinary conformal
field theory). However, numerical simulations show that this conjecture
works only under some specific conditions, not otherwise. I will explain
these observations using the ideas of replica trick to set up a
textbook-like renormalization flow analysis of random field models.