The Simons Foundation is pleased to announce the establishment of the Simons Collaboration on Global Categorical Symmetries, directed by Constantin Teleman of the University of California, Berkeley. This collaboration brings together a group of physicists and mathematicians, working across disciplinary boundaries, to unlock the power of symmetry in its broadest, most general form.
Symmetry is a powerful tool for organizing physical phenomena and anchors our understanding of the laws of nature. The notion of symmetry, however, has evolved dramatically since the emergence of groups and representations as the language for describing symmetries in geometry and mechanics. Galvanized most recently by advances in mathematics and physics, much of this evolution has been driven by the quest to achieve a deeper understanding of quantum field theory—the universal language of modern theoretical physics.
From a modern point of view, quantum field theory associates to every symmetry a topological defect, which acts on local and extended observables. This connection to topology has recently led to the discovery of new higher notions of symmetry, which in turn has shed new light on some of the most mysterious and profound phenomena described by quantum field theory, including color confinement in non-abelian gauge theories, duality and other phenomena.
The deep link between symmetry and topology finds its natural expression in the mathematics of topological quantum field theory, such as the modular tensor categories that describe invariants of knots and the long-distance physics of anyons. Recent advances have centered on the rich categorical structure of various defects and how it encodes the fundamental idea of locality, as expressed by the cobordism hypothesis. Our collaboration grows out of the synergy between these areas of physics and mathematics, weaving together cutting-edge developments.