Mini-course: "Quantum Models for Black Holes: Sachdev-Ye-Kitaev and generalizations" by Prof. Frank Ferrari

Aim: To introduce recently developed ideas and techniques on the SYK models and generalizations.

Description: Holography predicts that black holes can be described quantum mechanically by large N matrix models at strong coupling. We shall describe very recent ideas that have allowed to build exactly solvable models of this kind, providing an explicit quantum mechanical description of string-size black holes. These ideas are at the confluence of several different fields: condensed matter theory (disordered systems); quantum chaos; string theory and holography; matrix and tensor models (graph theory), etc. Many properties associated with black holes are found in the quantum mechanical description and will be discussed in the course, in particular the loss of unitarity at large N (and unitarity restoration at finite N), the quasi-normal behaviour, an emergent reparameterization invariance and maximal chaos.

Content:

1. Motivations from black hole physics and basic definitions of the models  (disordered, tensor, matrix versions);
2. Diagrammatrics and Schwinger-Dyson equations;
3. Two-point functions, possible IR behaviour and phase;
4. Four-point functions, chaos, Schwarzian effective action;
5. Topics from current research.

Date and Time:

• March 25^th, (Mon) 09:00-12:00;
             27^th, (Wed) 11:00-12:00;
             28^th, (Thu) 10:00-12:00.
• April 1^st, (Mon) 10:00-12:00;
           4^th, (Thu) 10:00-12:00;
           8^th, (Mon) 11:00-12:00;
         10^th, (Wed) 11:00-12:00;