Conformal mapping of non-Lorentzian geometries in SU(1, 2) Conformal Field Theory
Abstract We realize an explicit conformal mapping between the state and operator pictures in a class of (2 + 1)-dimensional non-Lorentzian field theories with SU(1, 2) × U(1) conformal symmetry. The state picture arises from null reducing four-dimensional relativistic conformal field theories on a t...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-03-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP03(2025)100 |
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| author | Stefano Baiguera Troels Harmark Yang Lei Ziqi Yan |
| author_facet | Stefano Baiguera Troels Harmark Yang Lei Ziqi Yan |
| author_sort | Stefano Baiguera |
| collection | DOAJ |
| description | Abstract We realize an explicit conformal mapping between the state and operator pictures in a class of (2 + 1)-dimensional non-Lorentzian field theories with SU(1, 2) × U(1) conformal symmetry. The state picture arises from null reducing four-dimensional relativistic conformal field theories on a three-sphere, yielding a non-Lorentzian geometry with the conformal Killing symmetry group SU(1, 2). This is complementary to the operator picture recently studied by Lambert et al. [1], where the geometry acquires an Ω-deformation. We then use the geometric mapping between the two pictures to derive a correspondence between the generators. This provides a concrete realization of the state-operator correspondence in non-Lorentzian conformal field theories. |
| format | Article |
| id | doaj-art-d6f07d850f2047c1aa0de9ab64ecd2b3 |
| institution | OA Journals |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-d6f07d850f2047c1aa0de9ab64ecd2b32025-08-20T02:11:57ZengSpringerOpenJournal of High Energy Physics1029-84792025-03-012025313810.1007/JHEP03(2025)100Conformal mapping of non-Lorentzian geometries in SU(1, 2) Conformal Field TheoryStefano Baiguera0Troels Harmark1Yang Lei2Ziqi Yan3INFN Sezione di PerugiaNiels Bohr International Academy, Niels Bohr Institute, University of CopenhagenInstitute for Advanced Study & School of Physical Science and Technology, Soochow UniversityNordita, KTH Royal Institute of Technology and Stockholm UniversityAbstract We realize an explicit conformal mapping between the state and operator pictures in a class of (2 + 1)-dimensional non-Lorentzian field theories with SU(1, 2) × U(1) conformal symmetry. The state picture arises from null reducing four-dimensional relativistic conformal field theories on a three-sphere, yielding a non-Lorentzian geometry with the conformal Killing symmetry group SU(1, 2). This is complementary to the operator picture recently studied by Lambert et al. [1], where the geometry acquires an Ω-deformation. We then use the geometric mapping between the two pictures to derive a correspondence between the generators. This provides a concrete realization of the state-operator correspondence in non-Lorentzian conformal field theories.https://doi.org/10.1007/JHEP03(2025)100Gauge-Gravity CorrespondenceScale and Conformal SymmetriesAdS-CFT Correspondence |
| spellingShingle | Stefano Baiguera Troels Harmark Yang Lei Ziqi Yan Conformal mapping of non-Lorentzian geometries in SU(1, 2) Conformal Field Theory Journal of High Energy Physics Gauge-Gravity Correspondence Scale and Conformal Symmetries AdS-CFT Correspondence |
| title | Conformal mapping of non-Lorentzian geometries in SU(1, 2) Conformal Field Theory |
| title_full | Conformal mapping of non-Lorentzian geometries in SU(1, 2) Conformal Field Theory |
| title_fullStr | Conformal mapping of non-Lorentzian geometries in SU(1, 2) Conformal Field Theory |
| title_full_unstemmed | Conformal mapping of non-Lorentzian geometries in SU(1, 2) Conformal Field Theory |
| title_short | Conformal mapping of non-Lorentzian geometries in SU(1, 2) Conformal Field Theory |
| title_sort | conformal mapping of non lorentzian geometries in su 1 2 conformal field theory |
| topic | Gauge-Gravity Correspondence Scale and Conformal Symmetries AdS-CFT Correspondence |
| url | https://doi.org/10.1007/JHEP03(2025)100 |
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