A new class of SYK-like models with maximal chaos

We investigate a model closely related to both the original Sachdev-Ye-Kitaev (SYK) model and the $\mathcal{N}=1$ supersymmetric SYK model. It consists of $N$ real Majorana fermions and $M$ auxiliary bosons with Yukawa interactions. We consider the large $N$ and $M$ limit and keep the ratio $M\mathrm{/}N$ fixed. The model has two branches characterized by the conformal dimensions of fields, which we compute as a function of the ratio $M\mathrm{/}N$. One of the branches contains the supersymmetric saddle for $M=N$. Furthermore, we determine the Lyapunov exponent of the model and find maximal chaos independent of $M\mathrm{/}N$.