  In this article, we study an elastic manifold in quenched disorder in the
limit of zero temperature. Naively it is equivalent to a free theory with
elasticity in Fourier-space proportional to k^4 instead of k^2, i.e. a model
without disorder in two space-dimensions less. This phenomenon, called
dimensional reduction, is most elegantly obtained using supersymmetry. However,
scaling arguments suggest, and functional renormalization shows that
dimensional reduction breaks down beyond the Larkin length. Thus one
equivalently expects a break-down of supersymmetry. Using methods of functional
renormalization, we show how supersymmetry is broken. We also discuss the
relation to replica-symmetry breaking, and how our formulation can be put into
work to lift apparent ambiguities in standard functional renormalization group
calculations.

Disordered Systems and Neural Networks