Séminaire de Physique Théorique
# Phase Diagram of Planar Matrix Quantum Mechanics, Tensor and SYK Models (arXiv: 1707.03431)

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Amphithéâtre Léon Motchane (IHES)
### Amphithéâtre Léon Motchane

#### IHES

35, route de Chartres, F-91440 Bures-sur-Yvette (France)

Description

In this talk I present the phase diagram of a U(N)^2 x O(D) invariant fermionic planar matrix quantum mechanics (equivalently tensor or complex SYK models) in the new large D limit dominated by melonic graphs. The Schwinger-Dyson equations can have two solutions describing either a "large" black hole phase a la SYK or a "small" black hole with trivial IR behavior. In the strongly coupled region of the mass-temperature plane, there is a line of first order phase transitions between the small and large black hole phases. This line terminates at a new critical point which can be studied numerically in detail. The critical exponents are non-mean-field and different on the two sides of the transition. If time allows, I will compare this to purely bosonic unstable and stable melonic models.

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