Logarithmic supertranslations and supertranslation-invariant Lorentz charges
Abstract We extend the BMS(4) group by adding logarithmic supertranslations. This is done by relaxing the boundary conditions on the metric and its conjugate momentum at spatial infinity in order to allow logarithmic terms of carefully designed form in the asymptotic expansion, while still preservin...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-02-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP02(2023)248 |
| _version_ | 1827900096707035136 |
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| author | Oscar Fuentealba Marc Henneaux Cédric Troessaert |
| author_facet | Oscar Fuentealba Marc Henneaux Cédric Troessaert |
| author_sort | Oscar Fuentealba |
| collection | DOAJ |
| description | Abstract We extend the BMS(4) group by adding logarithmic supertranslations. This is done by relaxing the boundary conditions on the metric and its conjugate momentum at spatial infinity in order to allow logarithmic terms of carefully designed form in the asymptotic expansion, while still preserving finiteness of the action. Standard theorems of the Hamiltonian formalism are used to derive the (finite) generators of the logarithmic supertranslations. As the ordinary supertranslations, these depend on a function of the angles. Ordinary and logarithmic supertranslations are then shown to form an abelian subalgebra with non-vanishing central extension. Because of this central term, one can make nonlinear redefinitions of the generators of the algebra so that the pure supertranslations (ℓ > 1 in a spherical harmonic expansion) and the logarithmic supertranslations have vanishing brackets with all the Poincaré generators, and, in particular, transform in the trivial representation of the Lorentz group. The symmetry algebra is then the direct sum of the Poincaré algebra and the infinite-dimensional abelian algebra formed by the pure supertranslations and the logarithmic supertranslations (with central extension). The pure supertranslations are thus completely decoupled from the standard Poincaré algebra in the asymptotic symmetry algebra. This implies in particular that one can provide a definition of the angular momentum which is manifestly free from supertranslation ambiguities. An intermediate redefinition providing a partial decoupling of the pure and logarithmic supertranslations is also given. |
| first_indexed | 2024-03-12T23:26:24Z |
| format | Article |
| id | doaj.art-a571313a482c462da962c1c9a3f13fdf |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-12T23:26:24Z |
| publishDate | 2023-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-a571313a482c462da962c1c9a3f13fdf2023-07-16T11:06:48ZengSpringerOpenJournal of High Energy Physics1029-84792023-02-012023215110.1007/JHEP02(2023)248Logarithmic supertranslations and supertranslation-invariant Lorentz chargesOscar Fuentealba0Marc Henneaux1Cédric Troessaert2Université Libre de Bruxelles and International Solvay InstitutesUniversité Libre de Bruxelles and International Solvay InstitutesHaute-Ecole Robert SchumanAbstract We extend the BMS(4) group by adding logarithmic supertranslations. This is done by relaxing the boundary conditions on the metric and its conjugate momentum at spatial infinity in order to allow logarithmic terms of carefully designed form in the asymptotic expansion, while still preserving finiteness of the action. Standard theorems of the Hamiltonian formalism are used to derive the (finite) generators of the logarithmic supertranslations. As the ordinary supertranslations, these depend on a function of the angles. Ordinary and logarithmic supertranslations are then shown to form an abelian subalgebra with non-vanishing central extension. Because of this central term, one can make nonlinear redefinitions of the generators of the algebra so that the pure supertranslations (ℓ > 1 in a spherical harmonic expansion) and the logarithmic supertranslations have vanishing brackets with all the Poincaré generators, and, in particular, transform in the trivial representation of the Lorentz group. The symmetry algebra is then the direct sum of the Poincaré algebra and the infinite-dimensional abelian algebra formed by the pure supertranslations and the logarithmic supertranslations (with central extension). The pure supertranslations are thus completely decoupled from the standard Poincaré algebra in the asymptotic symmetry algebra. This implies in particular that one can provide a definition of the angular momentum which is manifestly free from supertranslation ambiguities. An intermediate redefinition providing a partial decoupling of the pure and logarithmic supertranslations is also given.https://doi.org/10.1007/JHEP02(2023)248Classical Theories of GravityGlobal SymmetriesSpace-Time Symmetries |
| spellingShingle | Oscar Fuentealba Marc Henneaux Cédric Troessaert Logarithmic supertranslations and supertranslation-invariant Lorentz charges Journal of High Energy Physics Classical Theories of Gravity Global Symmetries Space-Time Symmetries |
| title | Logarithmic supertranslations and supertranslation-invariant Lorentz charges |
| title_full | Logarithmic supertranslations and supertranslation-invariant Lorentz charges |
| title_fullStr | Logarithmic supertranslations and supertranslation-invariant Lorentz charges |
| title_full_unstemmed | Logarithmic supertranslations and supertranslation-invariant Lorentz charges |
| title_short | Logarithmic supertranslations and supertranslation-invariant Lorentz charges |
| title_sort | logarithmic supertranslations and supertranslation invariant lorentz charges |
| topic | Classical Theories of Gravity Global Symmetries Space-Time Symmetries |
| url | https://doi.org/10.1007/JHEP02(2023)248 |
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