Generalized Fefferman-Graham gauge and boundary Weyl structures
Abstract In the framework of AdS/CFT correspondence, the Fefferman-Graham (FG) gauge offers a useful way to express asymptotically anti-de Sitter spaces, allowing a clear identification of their boundary structure. A known feature of this approach is that choosing a particular conformal representati...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-02-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP02(2025)007 |
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| author | Gabriel Arenas-Henriquez Felipe Diaz David Rivera-Betancour |
| author_facet | Gabriel Arenas-Henriquez Felipe Diaz David Rivera-Betancour |
| author_sort | Gabriel Arenas-Henriquez |
| collection | DOAJ |
| description | Abstract In the framework of AdS/CFT correspondence, the Fefferman-Graham (FG) gauge offers a useful way to express asymptotically anti-de Sitter spaces, allowing a clear identification of their boundary structure. A known feature of this approach is that choosing a particular conformal representative for the boundary metric breaks explicitly the boundary scaling symmetry. Recent developments have shown that it is possible to generalize the FG gauge to restore boundary Weyl invariance by adopting the Weyl-Fefferman-Graham gauge. In this paper, we focus on three-dimensional gravity and study the emergence of a boundary Weyl structure when considering the most general AdS boundary conditions introduced by Grumiller and Riegler [1]. We extend the holographic renormalization scheme to incorporate Weyl covariant quantities, identifying new subleading divergences appearing at the boundary. To address these, we introduce a new codimension-two counterterm, or corner term, that ensures the finiteness of the gravitational action. From here, we construct the quantum-generating functional, the holographic stress tensor, and compute the corresponding Weyl anomaly, showing that the latter is now expressed in a full Weyl covariant way. Finally, we discuss explicit applications to holographic integrable models and accelerating black holes. For the latter, we show that the new corner term plays a crucial role in the computation of the Euclidean on-shell action. |
| format | Article |
| id | doaj-art-c156ecf3d1344dc78aa6447e3e04e34f |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-c156ecf3d1344dc78aa6447e3e04e34f2025-02-09T12:08:55ZengSpringerOpenJournal of High Energy Physics1029-84792025-02-012025213210.1007/JHEP02(2025)007Generalized Fefferman-Graham gauge and boundary Weyl structuresGabriel Arenas-Henriquez0Felipe Diaz1David Rivera-Betancour2Yau Mathematical Sciences Center, Tsinghua UniversityInstitute for Theoretical and Mathematical Physics, Moscow State UniversityInstitute for Theoretical and Mathematical Physics, Moscow State UniversityAbstract In the framework of AdS/CFT correspondence, the Fefferman-Graham (FG) gauge offers a useful way to express asymptotically anti-de Sitter spaces, allowing a clear identification of their boundary structure. A known feature of this approach is that choosing a particular conformal representative for the boundary metric breaks explicitly the boundary scaling symmetry. Recent developments have shown that it is possible to generalize the FG gauge to restore boundary Weyl invariance by adopting the Weyl-Fefferman-Graham gauge. In this paper, we focus on three-dimensional gravity and study the emergence of a boundary Weyl structure when considering the most general AdS boundary conditions introduced by Grumiller and Riegler [1]. We extend the holographic renormalization scheme to incorporate Weyl covariant quantities, identifying new subleading divergences appearing at the boundary. To address these, we introduce a new codimension-two counterterm, or corner term, that ensures the finiteness of the gravitational action. From here, we construct the quantum-generating functional, the holographic stress tensor, and compute the corresponding Weyl anomaly, showing that the latter is now expressed in a full Weyl covariant way. Finally, we discuss explicit applications to holographic integrable models and accelerating black holes. For the latter, we show that the new corner term plays a crucial role in the computation of the Euclidean on-shell action.https://doi.org/10.1007/JHEP02(2025)007AdS-CFT CorrespondenceBlack HolesGauge-Gravity CorrespondenceScale and Conformal Symmetries |
| spellingShingle | Gabriel Arenas-Henriquez Felipe Diaz David Rivera-Betancour Generalized Fefferman-Graham gauge and boundary Weyl structures Journal of High Energy Physics AdS-CFT Correspondence Black Holes Gauge-Gravity Correspondence Scale and Conformal Symmetries |
| title | Generalized Fefferman-Graham gauge and boundary Weyl structures |
| title_full | Generalized Fefferman-Graham gauge and boundary Weyl structures |
| title_fullStr | Generalized Fefferman-Graham gauge and boundary Weyl structures |
| title_full_unstemmed | Generalized Fefferman-Graham gauge and boundary Weyl structures |
| title_short | Generalized Fefferman-Graham gauge and boundary Weyl structures |
| title_sort | generalized fefferman graham gauge and boundary weyl structures |
| topic | AdS-CFT Correspondence Black Holes Gauge-Gravity Correspondence Scale and Conformal Symmetries |
| url | https://doi.org/10.1007/JHEP02(2025)007 |
| work_keys_str_mv | AT gabrielarenashenriquez generalizedfeffermangrahamgaugeandboundaryweylstructures AT felipediaz generalizedfeffermangrahamgaugeandboundaryweylstructures AT davidriverabetancour generalizedfeffermangrahamgaugeandboundaryweylstructures |