Analyticity and the Unruh effect: a study of local modular flow
Abstract The Unruh effect can be formulated as the statement that the Minkowski vacuum in a Rindler wedge has a boost as its modular flow. In recent years, other examples of states with geometrically local modular flow have played important roles in understanding energy and entropy in quantum field...
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2024-09-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP09(2024)040 |
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| author | Jonathan Sorce |
| author_facet | Jonathan Sorce |
| author_sort | Jonathan Sorce |
| collection | DOAJ |
| description | Abstract The Unruh effect can be formulated as the statement that the Minkowski vacuum in a Rindler wedge has a boost as its modular flow. In recent years, other examples of states with geometrically local modular flow have played important roles in understanding energy and entropy in quantum field theory and quantum gravity. Here I initiate a general study of the settings in which geometric modular flow can arise, showing (i) that any geometric modular flow must be a conformal symmetry of the background spacetime, and (ii) that in a well behaved class of “weakly analytic” states, geometric modular flow must be future-directed. I further argue that if a geometric transformation is conformal but not isometric, then it can only be realized as modular flow in a conformal field theory. Finally, I discuss a few settings in which converse results can be shown — i.e., settings in which a state can be constructed whose modular flow reproduces a given vector field. |
| format | Article |
| id | doaj-art-1dbe6525f76d482a8769ef6dbc384b79 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-1dbe6525f76d482a8769ef6dbc384b792024-12-08T12:14:51ZengSpringerOpenJournal of High Energy Physics1029-84792024-09-012024914010.1007/JHEP09(2024)040Analyticity and the Unruh effect: a study of local modular flowJonathan Sorce0Center for Theoretical Physics, Massachusetts Institute of TechnologyAbstract The Unruh effect can be formulated as the statement that the Minkowski vacuum in a Rindler wedge has a boost as its modular flow. In recent years, other examples of states with geometrically local modular flow have played important roles in understanding energy and entropy in quantum field theory and quantum gravity. Here I initiate a general study of the settings in which geometric modular flow can arise, showing (i) that any geometric modular flow must be a conformal symmetry of the background spacetime, and (ii) that in a well behaved class of “weakly analytic” states, geometric modular flow must be future-directed. I further argue that if a geometric transformation is conformal but not isometric, then it can only be realized as modular flow in a conformal field theory. Finally, I discuss a few settings in which converse results can be shown — i.e., settings in which a state can be constructed whose modular flow reproduces a given vector field.https://doi.org/10.1007/JHEP09(2024)040Conformal and W SymmetryField Theories in Higher DimensionsSpace-Time Symmetries |
| spellingShingle | Jonathan Sorce Analyticity and the Unruh effect: a study of local modular flow Journal of High Energy Physics Conformal and W Symmetry Field Theories in Higher Dimensions Space-Time Symmetries |
| title | Analyticity and the Unruh effect: a study of local modular flow |
| title_full | Analyticity and the Unruh effect: a study of local modular flow |
| title_fullStr | Analyticity and the Unruh effect: a study of local modular flow |
| title_full_unstemmed | Analyticity and the Unruh effect: a study of local modular flow |
| title_short | Analyticity and the Unruh effect: a study of local modular flow |
| title_sort | analyticity and the unruh effect a study of local modular flow |
| topic | Conformal and W Symmetry Field Theories in Higher Dimensions Space-Time Symmetries |
| url | https://doi.org/10.1007/JHEP09(2024)040 |
| work_keys_str_mv | AT jonathansorce analyticityandtheunruheffectastudyoflocalmodularflow |