General relativity in three spacetime dimensions is a simplified model of gravity, possessing no local degrees of freedom, yet rich enough to admit black-hole solutions and other phenomena of interest. In the presence of a negative cosmological constant, the asymptotically anti–de Sitter (AdS) solutions admit a symmetry algebra consisting of two copies of the Virasoro algebra, with central charge inversely proportional to Newton’s constant. The study of this theory is greatly enriched by the AdS/CFT correspondence, which in this case implies a relationship to two-dimensional conformal field theory. General aspects of this theory can be understood by focusing on universal properties such as symmetries. The best understood examples of the AdS3/CFT2 correspondence arise from string theory constructions, in which case the gravity sector is accompanied by other propagating degrees of freedom. A question of recent interest is whether pure gravity can be made sense of as a quantum theory of gravity with a holographic dual. Attempting to answer this question requires making sense of the path integral over asymptotically AdS3 geometries.

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## AdS3 Gravity and Holography

### Per Kraus

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## Fluid–Gravity Correspondence

### Mukund Rangamani

The fluid–gravity correspondence establishes a detailed connection between solutions of relativistic dissipative hydrodynamics and black hole spacetimes that solve Einstein’s equations in a spacetime with negative cosmological constant. The correspondence can be seen as a natural corollary of the holographic anti–de Sitter (AdS)/conformal field theory (CFT) correspondence, which arises from string theory. The latter posits a quantum duality between gravitational dynamics in AdS spacetimes and that of a CFT in one dimension less. The fluid–gravity correspondence applies in the statistical thermodynamic limit of the CFT but can be viewed as an independent statement of a relation between two classic equations of physics: the relativistic Navier–Stokes equations and Einstein’s equations. The general structure of relativistic fluid dynamics is formulated in terms of conservation equations of energy–momentum and charges, supplemented with constitutive relations for the corresponding current densities. One can view this construction as an effective field theory for these conserved currents. This intuition applied to the gravitational equations of motion allows the solutions of relativistic hydrodynamics to be embedded as inhomogeneous, dynamical black holes in AdS spacetime.

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## Gravity and Quantum Entanglement

### Mukund Rangamani and Veronika Hubeny

The holographic entanglement entropy proposals give an explicit geometric encoding of spatially ordered quantum entanglement in continuum quantum field theory. These proposals have been developed in the context of the AdS/CFT correspondence, which posits a quantum duality between gravitational dynamics in anti-de Sitter (AdS) space times and that of a conformal field theory (CFT) in one fewer dimension. The von Neumann entropy of a spatial region of the CFT is given by the area of a particular extremal surface in the dual geometry. This surprising connection between a fundamental quantum mechanical concept and a simple geometric construct has given deep insights into the nature of the holographic map and potentially holds an important clue to unraveling the mysteries of quantum gravity.

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## Philosophy of Quantum Mechanics: Dynamical Collapse Theories

### Angelo Bassi

Quantum Mechanics is one of the most successful theories of nature. It accounts for all known properties of matter and light, and it does so with an unprecedented level of accuracy. On top of this, it generated many new technologies that now are part of daily life. In many ways, it can be said that we live in a quantum world. Yet, quantum theory is subject to an intense debate about its meaning as a theory of nature, which started from the very beginning and has never ended. The essence was captured by Schrödinger with the cat paradox: why do cats behave classically instead of being quantum like the one imagined by Schrödinger? Answering this question digs deep into the foundation of quantum mechanics.
A possible answer is Dynamical Collapse Theories. The fundamental assumption is that the Schrödinger equation, which is supposed to govern all quantum phenomena (at the non-relativistic level) is only approximately correct. It is an approximation of a nonlinear and stochastic dynamics, according to which the wave functions of microscopic objects can be in a superposition of different states because the nonlinear effects are negligible, while those of macroscopic objects are always very well localized in space because the nonlinear effects dominate for increasingly massive systems. Then, microscopic systems behave quantum mechanically, while macroscopic ones such as Schrödinger’s cat behave classically simply because the (newly postulated) laws of nature say so.
By changing the dynamics, collapse theories make predictions that are different from quantum-mechanical predictions. Then it becomes interesting to test the various collapse models that have been proposed. Experimental effort is increasing worldwide, so far limiting values of the theory’s parameters quantifying the collapse, since no collapse signal was detected, but possibly in the future finding such a signal and opening up a window beyond quantum theory.

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## Strange Metals and Black Holes: Insights From the Sachdev-Ye-Kitaev Model

### Subir Sachdev

Complex many-particle quantum entanglement is a central theme in two distinct major topics in physics: the strange metal state found in numerous correlated electron compounds and the quantum theory of black holes in Einstein gravity. The Sachdev-Ye-Kitaev model provides a solvable theory of entangled many-particle quantum states without quasiparticle excitations. This toy model has led to realistic universal models of strange metals and to new insights on the quantum states of black holes.

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## Supersymmetric QFT in Six Dimensions

### Alessandro Tomasiello

Quantum field theory (QFT) in six dimensions is more challenging than its four-dimensional counterpart: most models tend to become ill-defined at high energies. A combination of supersymmetry and string theory has yielded many QFTs that evade this problem and are low-energy effective manifestations of conformal field theories (CFTs). Besides the usual vector, spinor and scalar fields, the new ingredients are self-dual tensor fields, analogs of the electromagnetic field with an additional spacetime index, sometimes with an additional non-Abelian structure. A recent wave of interest in this field has produced several classification results, notably of models that have a holographic dual in string theory and of models that can be realized in F-theory. Several precise quantitative checks of the overall picture are now available, and give confidence that a full classification of all six-dimensional CFTs may be at hand.conformal field theories, supersymmetry, extra dimensions, holography, string theory, D-branes, F-theory