Supersymmetry method for interacting chaotic and disordered systems: the SYK model
The supersymmetry method was originally developed for studies of quantum phenomena in non-interacting disordered and chaotic systems.
I will report a step forward in this direction and develop the supersymmetry method for the Sachdev-Ye-Kitaev (SYK) model and other similar 0+1 dimensional interacting systems with disorder, where analytical techniques for quenched averaging have so far been based on the replica trick. As a demonstration of how the supersymmetry method works for such interacting systems, I will derive saddle point equations. In the semiclassical limit, the results are in agreement with those found using the replica technique. I will also discuss the formally exact superbosonized representation of the SYK model and argue that it paves the way for the precise calculation of the window of universality in which random matrix theory is applicable to the chaotic SYK system.