Counterterms, Kounterterms, and the variational problem in AdS gravity
Abstract We show that the Kounterterms for pure AdS gravity in arbitrary even dimensions coincide with the boundary counterterms obtained through holographic renormalization if and only if the boundary Weyl tensor vanishes. In particular, the Kounterterms lead to a well posed variational problem for...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2020-08-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP08(2020)061 |
| _version_ | 1829105755618279424 |
|---|---|
| author | Giorgos Anastasiou Olivera Miskovic Rodrigo Olea Ioannis Papadimitriou |
| author_facet | Giorgos Anastasiou Olivera Miskovic Rodrigo Olea Ioannis Papadimitriou |
| author_sort | Giorgos Anastasiou |
| collection | DOAJ |
| description | Abstract We show that the Kounterterms for pure AdS gravity in arbitrary even dimensions coincide with the boundary counterterms obtained through holographic renormalization if and only if the boundary Weyl tensor vanishes. In particular, the Kounterterms lead to a well posed variational problem for generic asymptotically locally AdS manifolds only in four dimensions. We determine the exact form of the counterterms for conformally flat boundaries and demonstrate that, in even dimensions, the Kounterterms take exactly the same form. This agreement can be understood as a consequence of Anderson’s theorem for the renormalized volume of conformally compact Einstein 4-manifolds and its higher dimensional generalizations by Albin and Chang, Qing and Yang. For odd dimensional asymptotically locally AdS manifolds with a conformally flat boundary, the Kounterterms coincide with the boundary counterterms except for the logarithmic divergence associated with the holographic conformal anomaly, and finite local terms. |
| first_indexed | 2024-12-12T06:12:10Z |
| format | Article |
| id | doaj.art-dda1e09930f042429cc5546ce0825a12 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-12T06:12:10Z |
| publishDate | 2020-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-dda1e09930f042429cc5546ce0825a122022-12-22T00:35:08ZengSpringerOpenJournal of High Energy Physics1029-84792020-08-012020815210.1007/JHEP08(2020)061Counterterms, Kounterterms, and the variational problem in AdS gravityGiorgos Anastasiou0Olivera Miskovic1Rodrigo Olea2Ioannis Papadimitriou3Instituto de Física, Pontificia Universidad Católica de ValparaísoInstituto de Física, Pontificia Universidad Católica de ValparaísoDepartamento de Ciencias Físicas, Universidad Andres BelloSchool of Physics, Korea Institute for Advanced StudyAbstract We show that the Kounterterms for pure AdS gravity in arbitrary even dimensions coincide with the boundary counterterms obtained through holographic renormalization if and only if the boundary Weyl tensor vanishes. In particular, the Kounterterms lead to a well posed variational problem for generic asymptotically locally AdS manifolds only in four dimensions. We determine the exact form of the counterterms for conformally flat boundaries and demonstrate that, in even dimensions, the Kounterterms take exactly the same form. This agreement can be understood as a consequence of Anderson’s theorem for the renormalized volume of conformally compact Einstein 4-manifolds and its higher dimensional generalizations by Albin and Chang, Qing and Yang. For odd dimensional asymptotically locally AdS manifolds with a conformally flat boundary, the Kounterterms coincide with the boundary counterterms except for the logarithmic divergence associated with the holographic conformal anomaly, and finite local terms.http://link.springer.com/article/10.1007/JHEP08(2020)061AdS-CFT CorrespondenceClassical Theories of GravityGauge-gravity correspondenceRenormalization Group |
| spellingShingle | Giorgos Anastasiou Olivera Miskovic Rodrigo Olea Ioannis Papadimitriou Counterterms, Kounterterms, and the variational problem in AdS gravity Journal of High Energy Physics AdS-CFT Correspondence Classical Theories of Gravity Gauge-gravity correspondence Renormalization Group |
| title | Counterterms, Kounterterms, and the variational problem in AdS gravity |
| title_full | Counterterms, Kounterterms, and the variational problem in AdS gravity |
| title_fullStr | Counterterms, Kounterterms, and the variational problem in AdS gravity |
| title_full_unstemmed | Counterterms, Kounterterms, and the variational problem in AdS gravity |
| title_short | Counterterms, Kounterterms, and the variational problem in AdS gravity |
| title_sort | counterterms kounterterms and the variational problem in ads gravity |
| topic | AdS-CFT Correspondence Classical Theories of Gravity Gauge-gravity correspondence Renormalization Group |
| url | http://link.springer.com/article/10.1007/JHEP08(2020)061 |
| work_keys_str_mv | AT giorgosanastasiou countertermskountertermsandthevariationalprobleminadsgravity AT oliveramiskovic countertermskountertermsandthevariationalprobleminadsgravity AT rodrigoolea countertermskountertermsandthevariationalprobleminadsgravity AT ioannispapadimitriou countertermskountertermsandthevariationalprobleminadsgravity |