Simons Collaboration on Global Categorical Symmetries

The Simons Foundation has announced 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.

Our collaboration builds on two broad classes of recent developments that radically changed the status of our fields over the past few years. On one hand, we have the development of the theory of topological orders which proved that topological quantum field theories (and their extended versions, TQFTs) are ubiquitous low energy approximations of gapped systems, leading to a classification of symmetry protected topological phases in TQFT language. On the other hand, we have a new perspective on global symmetries: the realization that in any quantum field theory (QFT) a global symmetry corresponds to a collection of topological defects, meaning that their support can be moved in spacetime without modifying the values of correlation functions, the property that ensures their conservation. This new perspective drastically alters the mathematical framework necessary to characterize symmetries, and it leads to a novel understanding of quantum numbers building upon recent developments in the context of extended topological field theories. This is an unprecedented opportunity to unveil novel powerful constraints on the dynamics of all physical systems that can be described via QFTs, and it is the central motivation for bridging our two communities.

Additional information about the focus of the collaboration is listed in the announcement. This is a preliminary webpage introducing the collaboration scientists. More information, detailing the work and activities of the collaboration, will be made available in due course.

The first meeting of the Collaboration will take place on October 11–13, at the Simons Center for Geometry and Physics.

Principal Investigators

	Ibrahima Bah works on holography, supergravity and string theory. He has developed novel methods and techniques for studying anomalies of continuous as well as discrete symmetries, for both conventional and generalized symmetries, for QFTs constructed within string theory.
	Mathew Bullimore works on mathematical structures in supersymmetric QFTs. He is known for contributions to symplectic duality via its incarnation in 3d N = 4 SCFTs and is currently studying categories of extended operators in twisted supersymmetric QFTs and their role in dualities.
	Alberto Cattaneo has developed important aspects of the perturbative quantization of gauge theories on manifolds with boundary and corners. This provides a new outlook on holography and residual symmetries on corners.
	Clay Córdova works on phases of quantum field theories, symmetry, and anomalies. His results include a proof of the a -theorem in a class of higher dimensional QFTs, developing new classes of higher group global symmetry, as well as new anomalies in QFTs, constraining the allowed mass gap
	Michele Del Zotto works at the interface of QFT, string theory, and math. He is a co-discoverer of many new (mostly non-Lagrangian) SCFTs in d ≥ 4, and he has studied the BPS spectra of such theories. He has pioneered the study of categorical symmetries in non-Lagrangian theories using geometric techniques.
	Thomas Dumitrescu works on strongly-coupled QFTs. He is known for the study of supersymmetric QFTs on curved manifolds, and (with Cordova and Intriligator) a supersymmetric a -theorem in 6d, a definitive account of SCFT representation theory, and the exploration of novel notions of global symmetry.
	Iñaki García Etxebarria works on QFT using geometry. He is a co-discoverer of N = 3 SCFTs in four dimensions. With collaborators Del Zotto, Ohmori, and others, he has connected categorical symmetries to geometry and applied modern approaches to anomalies in particle physics and string theory.
	Dan Freed works at the interface of geometry, topology, and QFT. With collaborators Hopkins, Moore, and Teleman, he has developed the concepts of invertible field theory, relative field theory, and flux non-commutativity, and has contributed to the classification of symmetry protected topological phases.
	Mike Hopkins ’s most important contributions have been in the development of chromatic homotopy theory, the solution of the Kervaire Invariant problem in the classification of manifolds, and a detailed classification of topological phases of matter, assuming invertibility and reflection positivity at low energy.
	Ken Intriligator works on QFT and the RG, applying symmetries to strongly-coupled QFTs. Jointly with Cordova and Dumitrescu he has classified unitary superconformal representations, established a supersymmetric a -theorem in 6d, and showed how certain anomalies give rise to 2-group global symmetries.
	Theo Johnson-Freyd ’s work on higher categories underpins global categorical symmetry, providing the first complete definition of fusion n -category and producing a mathematical equivalence between topological order and anomalous TQFT, thereby completing the classification of 3+1D topological orders.
	David Jordan has applied the global categorical symmetries of quantum groups, modular tensor categories, and their generalizations to study the Kapustin–Witten twist of N = 4 SUSY Yang–Mills, answering long-standing questions of Ben-Zvi, Bonahon–Wong, Freed–Teleman, and Witten.
	Julia Plavnik has worked extensively on the construction and classification of modular and super-modular tensor categories, most notably through the introduction of gauging and zesting for MTCs, which mathematically capture higher global symmetries on a QFT and lead to many new examples
	Nicolai Reshetikhin works in mathematical physics, mainly in QFT, representation theory and integrable systems. His most important contributions are to construction of the Reshetikhin–Turaev invariants of knots and 3-manifolds, and to the representation theory of quantum groups. His current research focus is to construct quantum field theories for manifolds with corners (in particular, topological and conformal field theories on such space times) and the gluing procedure for such quantum field theories.
	Constantin Teleman has made major contributions to the study of TQFTs in dimensions 2, 3, 4, and to gauge theory, boundary structures, and their consequences for topological phases of matter and lattice models, as well as Gromov- Witten theory, and many other physical theories of mathematical interest

Collaboration Associates

	Nitu Kitchloo is a homotopy theorist interested in applications to geometry and physics, most recently to link homology theories, and more generally to codimension-two defects in 4d QFT.
	Greg Moore works on the interaction of mathematics with string theory, QFT, and condensed matter, including the theory of Hitchin equations and Higgs bundles on surfaces, category theory (especially modular tensor categories), and analytic number theory. He is currently working with Freed on anomalies.
	Kantaro Ohmori is working on the role of symmetries in strongly-coupled QFTs. His work has focused on the applications of anomalies and (more recently) the use of global categorical symmetries to study the confining properties of adjoint QCD in 2d.
	Claudia Scheimbauer has constructed the higher category of E n -algebras, which model local observables and defects in QFT, and resulted in fundamental applications to Turaev–Viro/Barrett–Westbury, Crane–Yetter/Walker–Wang, and Witten–Reshetikhin–Turaev/Chern-Simons topological quantum field theories.
	Ryan Thorngren works at the interface of topology and physics. He has contributed to the development of higher-form symmetries, the cobordism classification of SPT phases and anomalies, and a generalization of Berry’s phase.