I will discuss the black hole solution dual to the BFSS matrix model in the 't Hooft limit. The classical physics of this black hole is invariant under a scale transformation, or ``similarity,'' that changes the action by an overall multiplicative factor, and is related to the peculiar temperature dependence of the entropy, $S \propto T^{9/5}$. The similarity fixes the masses of fluctuations around this background. This fact, as well as a mathematical trick where we view the solution as the dimensional reduction of an $AdS_{2 + 9/5} \times S^{8}$ geometry, allows for a simple computation of the black hole quasinormal modes.
I will then discuss an $\mathcal{N} = 2$ supersymmetric SYK model. The large $N$ equations for this model are a generalization of equations that have been previously studied as an unjustified truncation of the planar diagrams describing BFSS. This model has a peculiar low energy behavior in which the scalar fields develop large expectation values. In contrast to BFSS, it is found to have a ground state entropy and appears sub-maximally chaotic at low temperatures. While the initial motivation to study the model was based on similarities with BFSS, the physics looks fairly different.
Based on arXiv:2303.09974, arXiv:2309.08818.