  This note clarifies and extends results on the complex SYK model to the
solvable q = 2 case. We calculate the four point function OPE of fermions in
the low energy CFT, implying the existence of a tower of integer-weight
operators in the IR. We comment on the lack of a mode breaking conformal
symmetry in this special case of SYK and the consequences for deformations of
the theory near the conformal fixed point. We use the nearly-free structure of
the model to provide a closed form expression for OPE coefficients of the
integer-weight operators. We also discuss analytic and numerical results
relevant to the thermodynamics of q = 2 SYK in both the complex and real case.
The tower of operators transform in the discrete series of representations of
SL(2,R), the representations shared by dS2 and AdS2. In this work we continue
discussion of holographic models including these representations.
