Geometric approach to many-body quantum chaos

Quantum chaotic dynamics is in the focus of many current developments in physics, ranging from thermalisation in closed quantum systems to the black hole information puzzle. Recently, experimentalists have made great strides in controlling quantum dynamics, and theorists have developed solvable models to study many-body quantum chaos. To uncover what aspects of these results are universal and how different chaotic phenomena across time scales are related, a coherent framework unifying and extending recent developments is called for. This project will develop two new paradigms that unify different manifestations of quantum chaotic dynamics and bridge disciplines.In the quest for a common dynamical explanation of different chaotic phenomena, we will construct a Unified effective field theory (EFT) for chaos. In parallel, we will capitalise on the holographic Gauge/String duality that gives geometric insights into strongly coupled quantum dynamics to draw connections between gravity and chaos. By developing a holographic dictionary between the Unified EFT and gravity, we will build the Chaos/Gravity correspondence, a novel framework that uncovers how spacetime and its gravitational dynamics emerges from chaos in quantum field theories.Our methodology consists of exact analytical computations in solvable models, the study of chaotic phenomena in universal kinematic regimes, and the description of these results in the framework of EFT. These steps lay the foundations for conceptual leaps to the Unified EFT and the Chaos/Gravity correspondence that will be pursued in synergy. The two new paradigms will transform our understanding of many-body quantum chaos. The benefits of a systematic approach will be multifold: we will establish new quantitative relations between data characterising chaos, make experimental predictions about non-equilibrium phenomena at large system sizes, and potentially uncover new signatures of quantum chaos.