Tensor network approach to electromagnetic duality in (3+1)d topological gauge models
Abstract Given the Hamiltonian realisation of a topological (3+1)d gauge theory with finite group G, we consider a family of tensor network representations of its ground state subspace. This family is indexed by gapped boundary conditions encoded into module 2-categories over the input spherical fus...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-08-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP08(2022)149 |
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| author | Clement Delcamp |
| author_facet | Clement Delcamp |
| author_sort | Clement Delcamp |
| collection | DOAJ |
| description | Abstract Given the Hamiltonian realisation of a topological (3+1)d gauge theory with finite group G, we consider a family of tensor network representations of its ground state subspace. This family is indexed by gapped boundary conditions encoded into module 2-categories over the input spherical fusion 2-category. Individual tensors are characterised by symmetry conditions with respect to non-local operators acting on entanglement degrees of freedom. In the case of Dirichlet and Neumann boundary conditions, we show that the symmetry operators form the fusion 2-categories 2Vec G of G-graded 2-vector spaces and 2Rep(G) of 2-representations of G, respectively. In virtue of the Morita equivalence between 2VecG and 2Rep(G) — which we explicitly establish — the topological order can be realised as the Drinfel’d centre of either 2-category of operators; this is a realisation of the electromagnetic duality of the theory. Specialising to the case G = ℤ2, we recover tensor network representations that were recently introduced, as well as the relation between the electromagnetic duality of a pure ℤ2 gauge theory and the Kramers-Wannier duality of a boundary Ising model. |
| first_indexed | 2024-04-13T18:38:57Z |
| format | Article |
| id | doaj.art-5c1d8361cdc64dc0b663f7f828940cee |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-13T18:38:57Z |
| publishDate | 2022-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-5c1d8361cdc64dc0b663f7f828940cee2022-12-22T02:34:48ZengSpringerOpenJournal of High Energy Physics1029-84792022-08-012022813910.1007/JHEP08(2022)149Tensor network approach to electromagnetic duality in (3+1)d topological gauge modelsClement Delcamp0Max Planck Institute of Quantum OpticsAbstract Given the Hamiltonian realisation of a topological (3+1)d gauge theory with finite group G, we consider a family of tensor network representations of its ground state subspace. This family is indexed by gapped boundary conditions encoded into module 2-categories over the input spherical fusion 2-category. Individual tensors are characterised by symmetry conditions with respect to non-local operators acting on entanglement degrees of freedom. In the case of Dirichlet and Neumann boundary conditions, we show that the symmetry operators form the fusion 2-categories 2Vec G of G-graded 2-vector spaces and 2Rep(G) of 2-representations of G, respectively. In virtue of the Morita equivalence between 2VecG and 2Rep(G) — which we explicitly establish — the topological order can be realised as the Drinfel’d centre of either 2-category of operators; this is a realisation of the electromagnetic duality of the theory. Specialising to the case G = ℤ2, we recover tensor network representations that were recently introduced, as well as the relation between the electromagnetic duality of a pure ℤ2 gauge theory and the Kramers-Wannier duality of a boundary Ising model.https://doi.org/10.1007/JHEP08(2022)149Duality in Gauge Field TheoriesGauge SymmetryTopological States of Matter |
| spellingShingle | Clement Delcamp Tensor network approach to electromagnetic duality in (3+1)d topological gauge models Journal of High Energy Physics Duality in Gauge Field Theories Gauge Symmetry Topological States of Matter |
| title | Tensor network approach to electromagnetic duality in (3+1)d topological gauge models |
| title_full | Tensor network approach to electromagnetic duality in (3+1)d topological gauge models |
| title_fullStr | Tensor network approach to electromagnetic duality in (3+1)d topological gauge models |
| title_full_unstemmed | Tensor network approach to electromagnetic duality in (3+1)d topological gauge models |
| title_short | Tensor network approach to electromagnetic duality in (3+1)d topological gauge models |
| title_sort | tensor network approach to electromagnetic duality in 3 1 d topological gauge models |
| topic | Duality in Gauge Field Theories Gauge Symmetry Topological States of Matter |
| url | https://doi.org/10.1007/JHEP08(2022)149 |
| work_keys_str_mv | AT clementdelcamp tensornetworkapproachtoelectromagneticdualityin31dtopologicalgaugemodels |