| Project Detail |
High-symmetry structures in quantum field theories under study
Symmetry structures are key to deciphering the complexity of physical systems, especially those governed by quantum field theories (QFTs). They help group observables, classify phases, determine selection rules and offer insight into strongly coupled dynamics. Funded by the Marie Sklodowska-Curie Actions programme, the GEOSYM project will explore these symmetry structures in geometrically engineered QFTs. The focus will initially be on 4D theories defined by spectral curves and special holonomy spaces. The proposed research aims to define the symmetry representations and fusion structures related to their higher symmetries. This approach could offer insight into confining properties and phase structures of strongly coupled systems. Researchers will also study analogous symmetry structures for superconformal theories in 5D and 6D.
Symmetry structures are key to organizing the complexity of physical systems. In systems described by quantum field theories (QFTs) symmetries group observables, classify phases, determine selection rules and give insight into strongly coupled dynamics. They are irreplaceable in the study of phenomena such as confinement or duality. Recently, the notion of ‘symmetry’ in quantum field theories was understood to admit a substantial generalization to higher categorical structures such as n-groups and non-invertible symmetries. These realize further non-perturbative data yielding new handles in the study of QFTs. The goal of this project is to analyze such symmetry structures in geometrically engineered QFTs. We initially focus on theories in 4d parametrized by spectral curves and/or special holonomy spaces and aim to geometrize the symmetry representations and fusion structures related to their higher symmetries, building on both past work of the researcher and supervisor. This approach, unlike recent field theoretic developments, does not rely on a Lagrangian description of the QFT and therefore offers insight into confining properties and phase structures of strongly coupled systems. The foremost research objective of this proposal lies in charting these structures for increasingly less supersymmetric theories, including theories with no supersymmetry. All current evidence suggests that such symmetry structures only depend on topological data of the spectral curves and special holonomy space which we aim to trace through supersymmetry breaking deformations. Further research objectives include the study of analogous symmetry structures for superconformal theories in 5d and 6d. Such theories are intrinsically strongly coupled and the geometric methods developed in 4d, guided by field theory, come into their own as there are now no weak-coupling limits to extrapolate from. |
