# Overview

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Over the last fifteen years, our understanding of quantum gravity in string theory has been transformed by the discovery and exploitation of D-branes and the AdS/CFT correspondence in string theory. Many problems that were thought insuperably difficult have been solved, at least partially: (i) the entropy and thermodynamic properties of many extremal and near-extremal black holes have been precisely explained in terms of microscopic degrees of freedom, (ii) light has been shedon the physics of spacetime singularities, (iii) the holographic principle, positing massive reduction of the degrees of freedom in quantum gravity, has been understood precisely in spacetimes with a negative cosmological constant via a duality between gravity and gauge theory. This program of research has been so successful that it is now being used as a tool to shed light on otherwise intractable problems involving strongly coupled systems in other fields of physics.

In recent years, one of the focal point of much activity has been the study of certain toy models, in which typically both sides of the correspondence are amenable to an exact solution. One example are 2- and 3-dimensional models, in which gravity is non-dynamical (yet topologically non-trivial),while the field theory is completely integrable (e.g., 2-d minimal model CFTs). A rather different type of examples are vector-like field theories, which are conjecturally dual to higher-spin theories of gravity. In either instance, the basic idea is to exploit the fact that the reduced set of degrees of freedom is completely governed by a large symmetry algebra.

While there is a tremendous amount of evidence for the AdS/CFT correspondence, obtained through exactly solvable models or otherwise, the fundamental mechanisms behind such holographic behaviors remain unclear. The goal of this workshop is to elucidate them and to understand the limits to (or generality of) their applicability. In particular, we will address the following points:

–How general is holography?: To what extent do the above lessons rely on the particular constructions used to date? Are they tied to stringy effects and to string theory in particular, or are they general lessons for quantum gravity?

–The information paradox: Holography in string theory strongly suggests that information is not lost in black hole evaporation. Is it clear that this interpretation is correct? If so, how is this consistent with known bulk physics and the validity of Einstein gravity as a low-energy effective theory? How fast can information be extracted, under what conditions, and with what fidelity?

– The geometry of information: Why is the entropy of a black hole proportional to horizon area, and not to some other geometrical construct? In holographic contexts, how does the interior of a black hole (where information about the microstate is hidden) get represented in its holographically dual description as a state in a non- gravitating field theory? How can the thermodynamic properties of black holes and gravity be explained in flat space, far from extremality?

– Emergence of spacetime and locality: In the context of the gauge/gravity duality, can we give a constructive description of the emergence of additional spacetime dimensions as the effective description of strongly coupled field theory dynamics? How does spacetime locality emerge in this formulation? Can spacetime always be regarded as an emergent concept, or is this special to some classes of universes? How is locality in gravitational physics to be understood more broadly?

One of the goals of the workshop is to use the potential of recent progress on AdS/CFT to bring together mathematicians and physicists working on aspects of black hole physics ad AdS geometry.