On the New Large D Limit of Matrix Models and Phases of Matrix Quantum Mechanics and SYK Models

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In the first part of the talk, I will describe the new large N limit of tensor models, based on the “index” of graphs (in contrast to the standard large N expansion  based on the “degree”), and the associated new large D limit of matrix models. This new limit sheds an interesting light on the relation between disordered models à la SYK, tensor models and black holes. In the second part of the talk, I will apply these ideas to discuss the phase diagrams of some strongly coupled matrix quantum mechanics. The phase diagrams display many interesting features, including first and second order phase transitions and quantum critical points. Some of these phase transitions can be argued to provide a quantum mechanical description of the phenomenon of gravitational collapse.