The Higher Structure of Symmetries

ongoing

Quantum field theories (QFTs) are among the most powerful tools of modern theoretical physics, with wide applications from condensed matter to elementary particle physics, phase transitions, and quantum gravity. Over the past decade, and with tremendous progress over the past two years, QFT is undergoing a revolution: a generalized notion of symmetries, capable of giving conserved quantum numbers to extended field configurations, has emerged. Generalized symmetries are radically changing many aspects of the formalism, with applications ranging from the stability of impurities and defects in condensed matter systems, to the physics of hadrons in the standard model, as well as to the structures of phases. The hallmark of generalized symmetries is their higher structure, which encodes much more refined and sophisticated information about the QFT than that of ordinary symmetries. The goal of this reaserch proposal is to consolidate my research team, which will be devoted to develop and exploit the higher structure of symmetries to attack foundational open questions about QFT. In particular, in this project we will exploit the higher structures to obtain novel selection rules on QFT correlators, to constrain the behavior of quantum fields upon phase transitions and dualities, and most importantly to give new tools to study the behavior of QFTs across different energy scales along the flow of renormalization. To this end we are exploiting two different strategies. Firstly, we capitalize on the description of generalized symmetries as topological membranes, which allows the characterization of the higher structure via QFT correlators and topological field theory techniques. Secondly, we use a combination of tools ranging from dualities to higher dimensional QFT, and strings geometry, to probe regimes that are out of reach of more conventional methods. These strategies are complementary and intertwined.