Frank Ferrari, Université Libre de Bruxelles
On Melonic Matrix Models and SYK-like Black Holes
I will illustrate three aspects of the new large $D$ limit of matrix models and their applications to black hole physics:
- Graph theory aspect: I will review the basic properties of the new large $D$ limit of matrix models and provide a simple graph-theoretic argument for its existence, independent of standard tensor model techniques, using the concepts of Tait graphs and Petrie duals.
- Phase diagrams: I will outline the interesting phenomena found in the phase diagrams of simple fermionic matrix quantum mechanics/tensor/SYK models at strong coupling, 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.
- Probe analysis: I will briefly describe how the matrix point of view allows to naturally define models of D-particles probing an SYK-like black hole and discuss the qualitative properties of this class of models, emphasizing the difference between models based on fermionic and on bosonic strings. This approach provides an interesting strategy to study the emerging geometry of melonic/SYK black holes. In particular, it will be explained how a sharply defined notion of horizon emerges naturally.