Dynamical generalization of Yetter’s model based on a crossed module of discrete groups
Abstract We construct a lattice model based on a crossed module of possibly non-abelian finite groups. It generalizes known topological quantum field theories, but in contrast to these models admits local physical excitations. Its degrees of freedom are defined on links and plaquettes, while gauge t...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-03-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP03(2021)282 |
| _version_ | 1831543429656477696 |
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| author | Arkadiusz Bochniak Leszek Hadasz Błażej Ruba |
| author_facet | Arkadiusz Bochniak Leszek Hadasz Błażej Ruba |
| author_sort | Arkadiusz Bochniak |
| collection | DOAJ |
| description | Abstract We construct a lattice model based on a crossed module of possibly non-abelian finite groups. It generalizes known topological quantum field theories, but in contrast to these models admits local physical excitations. Its degrees of freedom are defined on links and plaquettes, while gauge transformations are based on vertices and links of the underlying lattice. We specify the Hilbert space, define basic observables (including the Hamiltonian) and initiate a discussion on the model’s phase diagram. The constructed model reduces in appropriate limits to topological theories with symmetries described by groups and crossed modules, lattice Yang-Mills theory and 2-form electrodynamics. We conclude by reviewing classifying spaces of crossed modules, with an emphasis on the direct relation between their geometry and properties of gauge theories under consideration. |
| first_indexed | 2024-12-17T00:51:07Z |
| format | Article |
| id | doaj.art-4d3b249a32da48608ec0c8ca53232e29 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-17T00:51:07Z |
| publishDate | 2021-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-4d3b249a32da48608ec0c8ca53232e292022-12-21T22:09:46ZengSpringerOpenJournal of High Energy Physics1029-84792021-03-012021315210.1007/JHEP03(2021)282Dynamical generalization of Yetter’s model based on a crossed module of discrete groupsArkadiusz Bochniak0Leszek Hadasz1Błażej Ruba2Institute of Theoretical Physics, Jagiellonian UniversityInstitute of Theoretical Physics, Jagiellonian UniversityInstitute of Theoretical Physics, Jagiellonian UniversityAbstract We construct a lattice model based on a crossed module of possibly non-abelian finite groups. It generalizes known topological quantum field theories, but in contrast to these models admits local physical excitations. Its degrees of freedom are defined on links and plaquettes, while gauge transformations are based on vertices and links of the underlying lattice. We specify the Hilbert space, define basic observables (including the Hamiltonian) and initiate a discussion on the model’s phase diagram. The constructed model reduces in appropriate limits to topological theories with symmetries described by groups and crossed modules, lattice Yang-Mills theory and 2-form electrodynamics. We conclude by reviewing classifying spaces of crossed modules, with an emphasis on the direct relation between their geometry and properties of gauge theories under consideration.https://doi.org/10.1007/JHEP03(2021)282Gauge SymmetryLattice Quantum Field TheoryTopological Field TheoriesTopological States of Matter |
| spellingShingle | Arkadiusz Bochniak Leszek Hadasz Błażej Ruba Dynamical generalization of Yetter’s model based on a crossed module of discrete groups Journal of High Energy Physics Gauge Symmetry Lattice Quantum Field Theory Topological Field Theories Topological States of Matter |
| title | Dynamical generalization of Yetter’s model based on a crossed module of discrete groups |
| title_full | Dynamical generalization of Yetter’s model based on a crossed module of discrete groups |
| title_fullStr | Dynamical generalization of Yetter’s model based on a crossed module of discrete groups |
| title_full_unstemmed | Dynamical generalization of Yetter’s model based on a crossed module of discrete groups |
| title_short | Dynamical generalization of Yetter’s model based on a crossed module of discrete groups |
| title_sort | dynamical generalization of yetter s model based on a crossed module of discrete groups |
| topic | Gauge Symmetry Lattice Quantum Field Theory Topological Field Theories Topological States of Matter |
| url | https://doi.org/10.1007/JHEP03(2021)282 |
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