Supersymmetry and metastability in disordered systems

The presence of metastable states is a well known feature of disordered systems and plays a crucial role in the slowing down of the dynamics and the occurrence of the glass transition. A deep understanding of the geometric structure of these states and its implications on the dynamical behaviour therefore represents a very important issue. We will show that when analyzing the properties of metastable states, and in particular their entropic contribution, a supersymmetry is revealed at a formal level, which has a clear physical interpretation. Systems that have different structures of metastable states seem to behave differently in terms of this supersymmetry: for some of them the supersymmetry is obeyed, for others it is spontaneously broken. We will discuss the physical meaning of the supersymmetry breaking and its connection with the cavity method.