Supersymmetry approach to interacting disordered systems: the SYK model

In this talk, we propose a new, supersymmetric sigma-model representation for interacting disordered fermion systems. To derive it, we decouple the interaction Hamiltonian using the conventional Hubbard-Stratonovich approach. Then we notice that the Hubbard-Stratonovich field can, in some situations, be gauged out from the denominator. This enables one to supersymmetrize the interacting theory. The new formalism is tested by calculating the fermion Green's function in the SYK model at large times and is argued to be effective for other interacting models with the disorder.