The Sachdev-Ye-Kitaev(SYK) models are quantum models of N fermions with random interactions. They are solvable in the large N limit. At low energy, they develop an emergent conformal symmetry and exhibit an extensive zero temperature entropy. And the out of time order correlators grow exponentially which gives maximal chaos. 

 

In these lectures, I will show how to derive and understand these properties. I will also introduce some generalizations of the model, including higher dimensional generalizations, complex fermions versions with U(1) symmetry, and supersymmetric generalizations etc. I will discuss some physical properties of the models which can also be obtained from holographic computations.

 

The four lectures will cover: the basic formalisms for the SYK model and zero-temperature entropy; Schwarzian effective action from the normal mode analysis; the Lyapunov exponent using Schwarzian action; and generalizations of the SYK models and verification of D~v^2/T.