Non-perturbative dynamics of quantum fields: from new deconfined phases of matter to quantum black holes

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When the degrees of freedom that constitute a quantum physical system are strongly coupled among each other, their collective low-energy behaviour can exhibit a plethora of exotic, surprising and unconventional phenomena. At the same time, however, our most sophisticated tool to describe the quantum world - quantum field theory - becomes extremely difficult to use. This problem appears across the board in many areas, from particle physics, to condensed matter physics, to astrophysics: strong coupling is an intrinsic complexity of quantum systems, whose solution can benefit disparate fields. A large variety of examples is provided by deconfined quantum states of matter, in which the collective behaviour gives rise to emergent low-energy degrees of freedom, often strongly coupled. Another context in which decrypting strong coupling can be the key to a breakthrough is quantum gravity: by the celebrated AdS/CFT correspondence, we can describe gravity in Anti-de-Sitter space in a fully-consistent quantum fashion, in terms of an ordinary - but strongly coupled - quantum field theory in one dimension less. The ambitious goal of this project is twofold: first, to develop innovative techniques to tame strong coupling; second, to exploit those techniques to discover new deconfined phases of matter on one side, and to unravel mysteries of quantum gravity and the quantum physics of black holes on the other side. I will follow several avenues in the quest for new computational tools at strong coupling, such as refining the concept of symmetry, developing supersymmetric localization, probing Borel summability of certain gauge theories. Applying these and other methods, I will systematically explore three-dimensional gauge theories with bosons and fermions, landscaping their phase diagrams and deconfined critical points. Meanwhile, I will extract the quantum entropy and other properties of black holes, exploring signatures of quantum effects to be compared with future experiments.