Emergent supersymmetry in condensed matter models of interacting Majorana fermions

It has been proposed that a superconductor in a magnetic 
field, in proximity to a topological insulator, has a Majorana fermion at the core of every vortex.  I will discuss the  phase diagram of this system with interactions between the Majorana fermions included. In the (1+1)  dimensional case the phase diagram has been well confirmed by a combination of analytical and  numerical methods.  It includes 3 non-trivial phases with emergent Lorentz invariance and a critical  point with Lorentz invariant supersymmetry. I will then discuss our conjecture on the 2 dimensional square vortex  lattice case, which also includes emergent Lorentz invariance and supersymmetry