  In this paper, we explore supersymmetric and 2d analogs of the SYK model. We
begin by working out a basis of (super)conformal eigenfunctions appropriate for
expanding a four-point function. We use this to clarify some details of the 1d
supersymmetric SYK model. We then introduce new bosonic and supersymmetric
analogs of SYK in two dimensions. These theories consist of $N$ fields
interacting with random $q$-field interactions. Although models built entirely
from bosons appear to be problematic, we find a supersymmetric model that flows
to a large $N$ CFT with interaction strength of order one. We derive an
integral formula for the four-point function at order $1/N$, and use it to
compute the central charge, chaos exponent and some anomalous dimensions. We
describe a problem that arises if one tries to find a 2d SYK-like CFT with a
continuous global symmetry.
