Logarithmic angle-dependent gauge transformations at null infinity
Abstract Logarithmic angle-dependent gauge transformations are symmetries of electromagnetism that are canonically conjugate to the standard O 1 $$ \mathcal{O}(1) $$ angle-dependent u(1) transformations. They were exhibited a few years ago at spatial infinity. In this paper, we derive their explicit...
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SpringerOpen
2025-07-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP07(2025)112 |
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| author | Oscar Fuentealba Marc Henneaux |
| author_facet | Oscar Fuentealba Marc Henneaux |
| author_sort | Oscar Fuentealba |
| collection | DOAJ |
| description | Abstract Logarithmic angle-dependent gauge transformations are symmetries of electromagnetism that are canonically conjugate to the standard O 1 $$ \mathcal{O}(1) $$ angle-dependent u(1) transformations. They were exhibited a few years ago at spatial infinity. In this paper, we derive their explicit form at null infinity. We also derive the expression there of the associated “conserved” surface integrals. To that end, we provide a comprehensive analysis of the behaviour of the electromagnetic vector potential A μ in the vicinity of null infinity for generic initial conditions given on a Cauchy hypersurface. This behaviour is given by a polylogarithmic expansion involving both gauge-invariant logarithmic terms also present in the field strengths and gauge-variant logarithmic terms with physical content, which we identify. We show on which explicit terms, and how, do the logarithmic angle-dependent gauge transformations act. Other results of this paper are a derivation of the matching conditions for the Goldstone boson and for the conserved charges of the angle-dependent u(1) asymptotic symmetries, as well as a clarification of a misconception concerning the non-existence of these angle-dependent u(1) charges in the presence of logarithms at null infinity. We also briefly comment on higher spacetime dimensions. |
| format | Article |
| id | doaj-art-e42dd6d19ce0421aa16fac7e4fa4db5e |
| institution | DOAJ |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-e42dd6d19ce0421aa16fac7e4fa4db5e2025-08-20T03:04:08ZengSpringerOpenJournal of High Energy Physics1029-84792025-07-012025715810.1007/JHEP07(2025)112Logarithmic angle-dependent gauge transformations at null infinityOscar Fuentealba0Marc Henneaux1Instituto de Ciencias Exactas y Naturales (ICEN), Universidad Arturo PratUniversité Libre de Bruxelles and International Solvay InstitutesAbstract Logarithmic angle-dependent gauge transformations are symmetries of electromagnetism that are canonically conjugate to the standard O 1 $$ \mathcal{O}(1) $$ angle-dependent u(1) transformations. They were exhibited a few years ago at spatial infinity. In this paper, we derive their explicit form at null infinity. We also derive the expression there of the associated “conserved” surface integrals. To that end, we provide a comprehensive analysis of the behaviour of the electromagnetic vector potential A μ in the vicinity of null infinity for generic initial conditions given on a Cauchy hypersurface. This behaviour is given by a polylogarithmic expansion involving both gauge-invariant logarithmic terms also present in the field strengths and gauge-variant logarithmic terms with physical content, which we identify. We show on which explicit terms, and how, do the logarithmic angle-dependent gauge transformations act. Other results of this paper are a derivation of the matching conditions for the Goldstone boson and for the conserved charges of the angle-dependent u(1) asymptotic symmetries, as well as a clarification of a misconception concerning the non-existence of these angle-dependent u(1) charges in the presence of logarithms at null infinity. We also briefly comment on higher spacetime dimensions.https://doi.org/10.1007/JHEP07(2025)112Gauge SymmetryGlobal SymmetriesSpace-Time Symmetries |
| spellingShingle | Oscar Fuentealba Marc Henneaux Logarithmic angle-dependent gauge transformations at null infinity Journal of High Energy Physics Gauge Symmetry Global Symmetries Space-Time Symmetries |
| title | Logarithmic angle-dependent gauge transformations at null infinity |
| title_full | Logarithmic angle-dependent gauge transformations at null infinity |
| title_fullStr | Logarithmic angle-dependent gauge transformations at null infinity |
| title_full_unstemmed | Logarithmic angle-dependent gauge transformations at null infinity |
| title_short | Logarithmic angle-dependent gauge transformations at null infinity |
| title_sort | logarithmic angle dependent gauge transformations at null infinity |
| topic | Gauge Symmetry Global Symmetries Space-Time Symmetries |
| url | https://doi.org/10.1007/JHEP07(2025)112 |
| work_keys_str_mv | AT oscarfuentealba logarithmicangledependentgaugetransformationsatnullinfinity AT marchenneaux logarithmicangledependentgaugetransformationsatnullinfinity |