TRIANGULAR SEMINAR: New techniques of large N and large D allow to study analytically planar matrix quantum mechanics at strong coupling in a reliable way. Using these techniques, we found a remarkable phase transition in these systems, which is very naturally interpreted as a quantum version of the phenomenon of black hole formation in a gravitational collapse.
Based on 1701.01171, 1707.03431, 1709.07366, 1710.07263 and work in progress.

In many instances of holographic correspondences between a d dimensional boundary theory and a d+1 dimensional bulk, a simple argument in the boundary theory implies that there must exist a direct relation between the on-shell Euclidean gravitational bulk action and the on-shell Euclidean action of a (d-1)-brane probing the bulk geometry. This relation is crucial for the consistency of holography but puzzling from the bulk perspective. We provide a full bulk derivation in the case of pure gravity. A central role is played by a non-trivial isoperimetric inequality that must be satisfied in a large class of Poincaré-Einstein spaces. Remarkably, this inequality follows from a theorem by John Lee.

We explain how to define, in matrix (gauge) field theory, the notion of the effective action of k ``probe'' branes in the presence of N ``background'' branes on which the field theory lives. The analysis of the large N planar diagram expansion which computes the effective action yields a simple and generic mechanism explaining the emergence of holographic space dimensions. The resulting effective action matches the non-abelian D-brane action in the closed string background dual to the field theory. We shall discuss briefly a few explicit examples, and also provide a general introduction to the notion of emerging space.