Linearization (in)stabilities and crossed products
Abstract Modular crossed product algebras have recently assumed an important role in perturbative quantum gravity as they lead to an intrinsic regularization of entanglement entropies by introducing quantum reference frames (QRFs) in place of explicit regulators. This is achieved by imposing certain...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-05-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP05(2025)211 |
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| author | Julian De Vuyst Stefan Eccles Philipp A. Höhn Josh Kirklin |
| author_facet | Julian De Vuyst Stefan Eccles Philipp A. Höhn Josh Kirklin |
| author_sort | Julian De Vuyst |
| collection | DOAJ |
| description | Abstract Modular crossed product algebras have recently assumed an important role in perturbative quantum gravity as they lead to an intrinsic regularization of entanglement entropies by introducing quantum reference frames (QRFs) in place of explicit regulators. This is achieved by imposing certain boost constraints on gravitons, QRFs and other fields. Here, we revisit the question of how these constraints should be understood through the lens of perturbation theory and particularly the study of linearization (in)stabilities, exploring when linearized solutions can be integrated to exact ones. Our aim is to provide some clarity about the status of justification, under various conditions, for imposing such constraints on the linearized theory in the G N → 0 limit as they turn out to be of second-order. While for spatially closed spacetimes there is an essentially unambiguous justification, in the presence of boundaries or the absence of isometries this depends on whether one is also interested in second-order observables. Linearization (in)stabilities occur in any gauge-covariant field theory with non-linear equations and to address this in a unified framework, we translate the subject from the usual canonical formulation into a systematic covariant phase space language. This overcomes theory-specific arguments, exhibiting the universal structure behind (in)stabilities, and permits us to cover arbitrary generally covariant theories. We comment on the relation to modular flow and illustrate our findings in several gravity and gauge theory examples. |
| format | Article |
| id | doaj-art-576c83af25ca4c4ab9528ca09fb00a71 |
| institution | OA Journals |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-576c83af25ca4c4ab9528ca09fb00a712025-08-20T02:05:45ZengSpringerOpenJournal of High Energy Physics1029-84792025-05-012025516910.1007/JHEP05(2025)211Linearization (in)stabilities and crossed productsJulian De Vuyst0Stefan Eccles1Philipp A. Höhn2Josh Kirklin3Qubits and Spacetime Unit, Okinawa Institute of Science and TechnologyQubits and Spacetime Unit, Okinawa Institute of Science and TechnologyQubits and Spacetime Unit, Okinawa Institute of Science and TechnologyPerimeter Institute for Theoretical PhysicsAbstract Modular crossed product algebras have recently assumed an important role in perturbative quantum gravity as they lead to an intrinsic regularization of entanglement entropies by introducing quantum reference frames (QRFs) in place of explicit regulators. This is achieved by imposing certain boost constraints on gravitons, QRFs and other fields. Here, we revisit the question of how these constraints should be understood through the lens of perturbation theory and particularly the study of linearization (in)stabilities, exploring when linearized solutions can be integrated to exact ones. Our aim is to provide some clarity about the status of justification, under various conditions, for imposing such constraints on the linearized theory in the G N → 0 limit as they turn out to be of second-order. While for spatially closed spacetimes there is an essentially unambiguous justification, in the presence of boundaries or the absence of isometries this depends on whether one is also interested in second-order observables. Linearization (in)stabilities occur in any gauge-covariant field theory with non-linear equations and to address this in a unified framework, we translate the subject from the usual canonical formulation into a systematic covariant phase space language. This overcomes theory-specific arguments, exhibiting the universal structure behind (in)stabilities, and permits us to cover arbitrary generally covariant theories. We comment on the relation to modular flow and illustrate our findings in several gravity and gauge theory examples.https://doi.org/10.1007/JHEP05(2025)211Gauge SymmetrySpace-Time SymmetriesClassical Theories of GravityGlobal Symmetries |
| spellingShingle | Julian De Vuyst Stefan Eccles Philipp A. Höhn Josh Kirklin Linearization (in)stabilities and crossed products Journal of High Energy Physics Gauge Symmetry Space-Time Symmetries Classical Theories of Gravity Global Symmetries |
| title | Linearization (in)stabilities and crossed products |
| title_full | Linearization (in)stabilities and crossed products |
| title_fullStr | Linearization (in)stabilities and crossed products |
| title_full_unstemmed | Linearization (in)stabilities and crossed products |
| title_short | Linearization (in)stabilities and crossed products |
| title_sort | linearization in stabilities and crossed products |
| topic | Gauge Symmetry Space-Time Symmetries Classical Theories of Gravity Global Symmetries |
| url | https://doi.org/10.1007/JHEP05(2025)211 |
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