Carroll symmetries in field theory and gravity

Abstract: This thesis explores several facets of Carroll symmetries through their applications to field theories and gravity. The geometric description of curved Carroll manifolds is developed from a Cartan-geometric viewpoint, reviewed at the outset. On these backgrounds, we study various field theories, including scalar and vector Carroll swiftons. Imposing causality and locality, we derive a universal sector of the commutators between Carroll stress-energy tensor components valid for any Carroll quantum field theory. In two dimensions, we confirm the connection to holography by showing that a Carroll boost anomaly gives rise to additional Schwinger-like terms in these brackets, sourcing the familiar central extensions of the asymptotic symmetries of three-dimensional asymptotically flat Einstein gravity. Afterwards, we come to theories of Carroll gravity which, as we argue, provide a valuable playground for understanding quantum gravity in a specific scaling limit which we refer to as the tantum gravity limit. At first, we review Carroll gravity in general dimensions and subsequently restrict to two spacetime dimensions where we introduce Carroll dilaton gravity. We define Carroll black holes as massive vacuum solutions to these theories that admit well-defined thermodynamic properties but have a Carroll extremal surface instead of an event horizon. After investigating several models and their solutions we finally add quantum matter to these backgrounds and study how the thermodynamic properties of a Carroll black hole reflect in its vacuum states. For the Carroll-Schwarzschild black hole we find a non-vanishing asymptotic energy density. We refer to this phenomenon as the Carroll-Hawking effect.