Representation theory of solitons
Abstract Solitons in two-dimensional quantum field theory exhibit patterns of degeneracies and associated selection rules on scattering amplitudes. We develop a representation theory that captures these intriguing features of solitons. This representation theory is based on an algebra we refer to as...
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| Language: | English |
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SpringerOpen
2025-06-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP06(2025)001 |
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| author | Clay Córdova Nicholas Holfester Kantaro Ohmori |
| author_facet | Clay Córdova Nicholas Holfester Kantaro Ohmori |
| author_sort | Clay Córdova |
| collection | DOAJ |
| description | Abstract Solitons in two-dimensional quantum field theory exhibit patterns of degeneracies and associated selection rules on scattering amplitudes. We develop a representation theory that captures these intriguing features of solitons. This representation theory is based on an algebra we refer to as the strip algebra, Str C M $$ {\textbf{Str}}_{\mathcal{C}}\left(\mathcal{M}\right) $$ , which is defined in terms of the non-invertible symmetry, C $$ \mathcal{C} $$ , a fusion category, and its action on boundary conditions encoded by a module category, M $$ \mathcal{M} $$ . The strip algebra is a C ∗-weak Hopf algebra, a fact which can be elegantly deduced by quantizing the three-dimensional Drinfeld center TQFT, Z C $$ \mathcal{Z}\left(\mathcal{C}\right) $$ , on a spatial manifold with corners. These structures imply that the representation category of the strip algebra is also a unitary fusion category which we identify with a dual category C M ∗ $$ {\mathcal{C}}_{\mathcal{M}}^{\ast } $$ . We present a straightforward method for analyzing these representations in terms of quiver diagrams where nodes are vacua and arrows are solitons and provide examples demonstrating how the representation theory reproduces known degeneracies and selection rules of soliton scattering. Our analysis provides the general framework for analyzing non-invertible symmetry on manifolds with boundary and applies both to the case of boundaries at infinity, relevant to particle physics, and boundaries at finite distance, relevant in conformal field theory or condensed matter systems. |
| format | Article |
| id | doaj-art-516626d50f2d4f558b62f11495acf7e5 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-516626d50f2d4f558b62f11495acf7e52025-08-20T04:01:43ZengSpringerOpenJournal of High Energy Physics1029-84792025-06-012025615810.1007/JHEP06(2025)001Representation theory of solitonsClay Córdova0Nicholas Holfester1Kantaro Ohmori2Kadanoff Center for Theoretical Physics & Enrico Fermi Institute, University of ChicagoKadanoff Center for Theoretical Physics & Enrico Fermi Institute, University of ChicagoFaculty of Science, University of TokyoAbstract Solitons in two-dimensional quantum field theory exhibit patterns of degeneracies and associated selection rules on scattering amplitudes. We develop a representation theory that captures these intriguing features of solitons. This representation theory is based on an algebra we refer to as the strip algebra, Str C M $$ {\textbf{Str}}_{\mathcal{C}}\left(\mathcal{M}\right) $$ , which is defined in terms of the non-invertible symmetry, C $$ \mathcal{C} $$ , a fusion category, and its action on boundary conditions encoded by a module category, M $$ \mathcal{M} $$ . The strip algebra is a C ∗-weak Hopf algebra, a fact which can be elegantly deduced by quantizing the three-dimensional Drinfeld center TQFT, Z C $$ \mathcal{Z}\left(\mathcal{C}\right) $$ , on a spatial manifold with corners. These structures imply that the representation category of the strip algebra is also a unitary fusion category which we identify with a dual category C M ∗ $$ {\mathcal{C}}_{\mathcal{M}}^{\ast } $$ . We present a straightforward method for analyzing these representations in terms of quiver diagrams where nodes are vacua and arrows are solitons and provide examples demonstrating how the representation theory reproduces known degeneracies and selection rules of soliton scattering. Our analysis provides the general framework for analyzing non-invertible symmetry on manifolds with boundary and applies both to the case of boundaries at infinity, relevant to particle physics, and boundaries at finite distance, relevant in conformal field theory or condensed matter systems.https://doi.org/10.1007/JHEP06(2025)001Field Theories in Lower DimensionsGlobal SymmetriesQuantum GroupsSolitons Monopoles and Instantons |
| spellingShingle | Clay Córdova Nicholas Holfester Kantaro Ohmori Representation theory of solitons Journal of High Energy Physics Field Theories in Lower Dimensions Global Symmetries Quantum Groups Solitons Monopoles and Instantons |
| title | Representation theory of solitons |
| title_full | Representation theory of solitons |
| title_fullStr | Representation theory of solitons |
| title_full_unstemmed | Representation theory of solitons |
| title_short | Representation theory of solitons |
| title_sort | representation theory of solitons |
| topic | Field Theories in Lower Dimensions Global Symmetries Quantum Groups Solitons Monopoles and Instantons |
| url | https://doi.org/10.1007/JHEP06(2025)001 |
| work_keys_str_mv | AT claycordova representationtheoryofsolitons AT nicholasholfester representationtheoryofsolitons AT kantaroohmori representationtheoryofsolitons |