Scale and conformal invariance in 2d σ-models, with an application to $$\mathcal{N}$$ = 4 supersymmetry
Abstract By adapting previously known arguments concerning Ricci flow and the c-theorem, we give a direct proof that in a two-dimensional sigma-model with compact target space, scale invariance implies conformal invariance in perturbation theory. This argument, which applies to a general sigma-model...
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| Format: | Article |
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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)056 |
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| author | Georgios Papadopoulos Edward Witten |
| author_facet | Georgios Papadopoulos Edward Witten |
| author_sort | Georgios Papadopoulos |
| collection | DOAJ |
| description | Abstract By adapting previously known arguments concerning Ricci flow and the c-theorem, we give a direct proof that in a two-dimensional sigma-model with compact target space, scale invariance implies conformal invariance in perturbation theory. This argument, which applies to a general sigma-model constructed with a target space metric and B-field, is in accord with a more general proof in the literature that applies to arbitrary two-dimensional quantum field theories. Models with extended supersymmetry and a B-field are known to provide interesting test cases for the relation between scale invariance and conformal invariance in sigma-model perturbation theory. We give examples showing that in such models, the obstructions to conformal invariance suggested by general arguments can actually occur in models with target spaces that are not compact or complete. Thus compactness of the target space, or at least a suitable condition of completeness, is necessary as well as sufficient to ensure that scale invariance implies conformal invariance in models of this type. |
| format | Article |
| id | doaj-art-d5f095a89395482e9becddf8244f912b |
| 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-d5f095a89395482e9becddf8244f912b2025-08-20T02:16:06ZengSpringerOpenJournal of High Energy Physics1029-84792025-03-012025313110.1007/JHEP03(2025)056Scale and conformal invariance in 2d σ-models, with an application to $$\mathcal{N}$$ = 4 supersymmetryGeorgios Papadopoulos0Edward Witten1Department of Mathematics, King’s College LondonSchool of Natural Sciences, Institute for Advanced StudyAbstract By adapting previously known arguments concerning Ricci flow and the c-theorem, we give a direct proof that in a two-dimensional sigma-model with compact target space, scale invariance implies conformal invariance in perturbation theory. This argument, which applies to a general sigma-model constructed with a target space metric and B-field, is in accord with a more general proof in the literature that applies to arbitrary two-dimensional quantum field theories. Models with extended supersymmetry and a B-field are known to provide interesting test cases for the relation between scale invariance and conformal invariance in sigma-model perturbation theory. We give examples showing that in such models, the obstructions to conformal invariance suggested by general arguments can actually occur in models with target spaces that are not compact or complete. Thus compactness of the target space, or at least a suitable condition of completeness, is necessary as well as sufficient to ensure that scale invariance implies conformal invariance in models of this type.https://doi.org/10.1007/JHEP03(2025)056Field Theories in Lower DimensionsScale and Conformal SymmetriesSigma ModelsConformal Field Models in String Theory |
| spellingShingle | Georgios Papadopoulos Edward Witten Scale and conformal invariance in 2d σ-models, with an application to $$\mathcal{N}$$ = 4 supersymmetry Journal of High Energy Physics Field Theories in Lower Dimensions Scale and Conformal Symmetries Sigma Models Conformal Field Models in String Theory |
| title | Scale and conformal invariance in 2d σ-models, with an application to $$\mathcal{N}$$ = 4 supersymmetry |
| title_full | Scale and conformal invariance in 2d σ-models, with an application to $$\mathcal{N}$$ = 4 supersymmetry |
| title_fullStr | Scale and conformal invariance in 2d σ-models, with an application to $$\mathcal{N}$$ = 4 supersymmetry |
| title_full_unstemmed | Scale and conformal invariance in 2d σ-models, with an application to $$\mathcal{N}$$ = 4 supersymmetry |
| title_short | Scale and conformal invariance in 2d σ-models, with an application to $$\mathcal{N}$$ = 4 supersymmetry |
| title_sort | scale and conformal invariance in 2d σ models with an application to mathcal n 4 supersymmetry |
| topic | Field Theories in Lower Dimensions Scale and Conformal Symmetries Sigma Models Conformal Field Models in String Theory |
| url | https://doi.org/10.1007/JHEP03(2025)056 |
| work_keys_str_mv | AT georgiospapadopoulos scaleandconformalinvariancein2dsmodelswithanapplicationtomathcaln4supersymmetry AT edwardwitten scaleandconformalinvariancein2dsmodelswithanapplicationtomathcaln4supersymmetry |