No U(1) ‘electric-magnetic’ duality in Einstein gravity
Abstract We revisit the question of whether classical general relativity obeys, beyond the linearised order, an analogue of the global U(1) electric-magnetic duality of Maxwell theory, with the Riemann tensor playing the role analogous to the field strength. Following contradictory claims in the lit...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-04-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP04(2024)093 |
| _version_ | 1797199713392394240 |
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| author | Ricardo Monteiro |
| author_facet | Ricardo Monteiro |
| author_sort | Ricardo Monteiro |
| collection | DOAJ |
| description | Abstract We revisit the question of whether classical general relativity obeys, beyond the linearised order, an analogue of the global U(1) electric-magnetic duality of Maxwell theory, with the Riemann tensor playing the role analogous to the field strength. Following contradictory claims in the literature, we present a simple gauge-invariant argument that the duality does not hold. The duality condition is the conservation of the helicity charge. Scattering amplitudes of gravitons in general relativity, and of gluons in Yang-Mills theory, violate this selection rule already at tree level. Indeed, the maximally-helicity-violating (MHV) amplitudes are famous for their simplicity. The duality in the linearised theories is, therefore, broken by the interactions. In contrast, the tree-level scattering amplitudes in duality-invariant theories of non-linear electromagnetism are known to obey helicity conservation. While the duality is not a symmetry of the full theory of general relativity, it does hold within a sector of the solution space, including vacuum type D solutions, where the duality is known to rotate between mass and NUT charge. |
| first_indexed | 2024-04-24T07:20:08Z |
| format | Article |
| id | doaj.art-d27e5dbc52be45f48f1b411075446dae |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-24T07:20:08Z |
| publishDate | 2024-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-d27e5dbc52be45f48f1b411075446dae2024-04-21T11:07:01ZengSpringerOpenJournal of High Energy Physics1029-84792024-04-012024411710.1007/JHEP04(2024)093No U(1) ‘electric-magnetic’ duality in Einstein gravityRicardo Monteiro0Centre for Theoretical Physics, Department of Physics and Astronomy, Queen Mary University of LondonAbstract We revisit the question of whether classical general relativity obeys, beyond the linearised order, an analogue of the global U(1) electric-magnetic duality of Maxwell theory, with the Riemann tensor playing the role analogous to the field strength. Following contradictory claims in the literature, we present a simple gauge-invariant argument that the duality does not hold. The duality condition is the conservation of the helicity charge. Scattering amplitudes of gravitons in general relativity, and of gluons in Yang-Mills theory, violate this selection rule already at tree level. Indeed, the maximally-helicity-violating (MHV) amplitudes are famous for their simplicity. The duality in the linearised theories is, therefore, broken by the interactions. In contrast, the tree-level scattering amplitudes in duality-invariant theories of non-linear electromagnetism are known to obey helicity conservation. While the duality is not a symmetry of the full theory of general relativity, it does hold within a sector of the solution space, including vacuum type D solutions, where the duality is known to rotate between mass and NUT charge.https://doi.org/10.1007/JHEP04(2024)093Classical Theories of GravityGlobal SymmetriesScattering Amplitudes |
| spellingShingle | Ricardo Monteiro No U(1) ‘electric-magnetic’ duality in Einstein gravity Journal of High Energy Physics Classical Theories of Gravity Global Symmetries Scattering Amplitudes |
| title | No U(1) ‘electric-magnetic’ duality in Einstein gravity |
| title_full | No U(1) ‘electric-magnetic’ duality in Einstein gravity |
| title_fullStr | No U(1) ‘electric-magnetic’ duality in Einstein gravity |
| title_full_unstemmed | No U(1) ‘electric-magnetic’ duality in Einstein gravity |
| title_short | No U(1) ‘electric-magnetic’ duality in Einstein gravity |
| title_sort | no u 1 electric magnetic duality in einstein gravity |
| topic | Classical Theories of Gravity Global Symmetries Scattering Amplitudes |
| url | https://doi.org/10.1007/JHEP04(2024)093 |
| work_keys_str_mv | AT ricardomonteiro nou1electricmagneticdualityineinsteingravity |