Quantum complexity in Quantum Field Theory and Holography

The late time behaviour and the approach towards thermalistaion in many-body quantum systems is a topic with a long-standing history and one of the deep open questions in the dynamics of quantum field theories. The holographic correspondence between semiclassical gravity and strongly-interacting quantum field theories adds a completely new dimension to this problem by directly relating to the process of formation and evolution of black holes in asymptotically Anti-de-Sitter spacetimes. Recently our understanding of thermalisation and late time asympototics of QFTs has been questioned by the emergence of a new notion- that of holographic quantum complexity which is being argued to equilibrate on times scales exponentially larger than standard thermalisation times. The implications of this conjecture are yet to be completely understood. The aim of this project is to understand and build the notion of quantum complexity in quantum field theory from first principles in weakly interacting quantum systems and then systematically progress towards strongly interacting ones, to finally enable us to make contact with current proposals (Action/Volume) for holographic quantum complexity. We expect to address and analyse many new questions regrding WFT dynamics and black hole evolution along the way.