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.
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.
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