Chaos in Field Theory and Gravity

Abstract

The fate of information contained in an object when it falls into a black hole has been a matter of debate since Hawking’s discovery that all black holes emit radiation and can eventually evaporate away. Though there has been no complete resolution to the black hole information puzzle, it is now widely accepted that black holes do not destroy information and that one can, at least in principle, recover this information from the radiation. As it turns out, the relevant time scale for this recovery is the time required by the black hole to scramble the information over its degrees of freedom. This result has led to an ongoing fruitful exchange of ideas between quantum chaos, quantum information, quantum matter and black hole physics, which we discuss and attempt to summarise in this thesis. Field theories, especially the ones that are solvable, will be another focus of this thesis. In particular, we discuss two such models, the Sachdev-Ye-Kitaev (SYK) model and one of its variants, the charged SYK model, a generalised version of the SYK model with Dirac fermions, with a global U(1) symmetry. We also provide a new derivation for the effective action of the charged SYK model.