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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## 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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## 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