On the resilience of the gravitational variational principle under renormalization
Abstract A well-defined variational principle for gravitational actions typically requires to cancel boundary terms produced by the variation of the bulk action with a suitable set of boundary counterterms. This can be achieved by carefully balancing the coefficients multiplying the bulk operators w...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-10-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP10(2023)054 |
| _version_ | 1797341410833203200 |
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| author | Giulio Neri Stefano Liberati |
| author_facet | Giulio Neri Stefano Liberati |
| author_sort | Giulio Neri |
| collection | DOAJ |
| description | Abstract A well-defined variational principle for gravitational actions typically requires to cancel boundary terms produced by the variation of the bulk action with a suitable set of boundary counterterms. This can be achieved by carefully balancing the coefficients multiplying the bulk operators with those multiplying the boundary ones. A typical example of this construction is the Gibbons-Hawking-York boundary action that needs to be added to the Einstein-Hilbert one in order to have a well-defined metric variation for General Relativity with Dirichlet boundary conditions. Quantum fluctuations of matter fields lead to a renormalization of these coefficients which may or may not preserve this balance. Indeed, already at the level of General Relativity, the resilience of the matching between bulk and boundary constants is far from obvious and it is anyway incomplete given that matter generically induces quadratic curvature operators. We investigate here the resilience of the matching of higher-order couplings upon renormalization by a non-minimally coupled scalar field and show that a problem is present. Even though we do not completely solve the latter, we show that it can be greatly ameliorated by a wise splitting between dynamical and topological contributions. Doing so, we find that the bulk-boundary matching is preserved up to a universal term (present for any Weyl invariant matter field content), whose nature and possible cancellation we shall discuss in the end. |
| first_indexed | 2024-03-08T10:17:42Z |
| format | Article |
| id | doaj.art-5c62d6b242ef4f1c8aee645a256636df |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-08T10:17:42Z |
| publishDate | 2023-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-5c62d6b242ef4f1c8aee645a256636df2024-01-28T12:14:55ZengSpringerOpenJournal of High Energy Physics1029-84792023-10-0120231012810.1007/JHEP10(2023)054On the resilience of the gravitational variational principle under renormalizationGiulio Neri0Stefano Liberati1International School for Advanced Studies (SISSA)International School for Advanced Studies (SISSA)Abstract A well-defined variational principle for gravitational actions typically requires to cancel boundary terms produced by the variation of the bulk action with a suitable set of boundary counterterms. This can be achieved by carefully balancing the coefficients multiplying the bulk operators with those multiplying the boundary ones. A typical example of this construction is the Gibbons-Hawking-York boundary action that needs to be added to the Einstein-Hilbert one in order to have a well-defined metric variation for General Relativity with Dirichlet boundary conditions. Quantum fluctuations of matter fields lead to a renormalization of these coefficients which may or may not preserve this balance. Indeed, already at the level of General Relativity, the resilience of the matching between bulk and boundary constants is far from obvious and it is anyway incomplete given that matter generically induces quadratic curvature operators. We investigate here the resilience of the matching of higher-order couplings upon renormalization by a non-minimally coupled scalar field and show that a problem is present. Even though we do not completely solve the latter, we show that it can be greatly ameliorated by a wise splitting between dynamical and topological contributions. Doing so, we find that the bulk-boundary matching is preserved up to a universal term (present for any Weyl invariant matter field content), whose nature and possible cancellation we shall discuss in the end.https://doi.org/10.1007/JHEP10(2023)054Classical Theories of GravityRenormalization and RegularizationRenormalization Group |
| spellingShingle | Giulio Neri Stefano Liberati On the resilience of the gravitational variational principle under renormalization Journal of High Energy Physics Classical Theories of Gravity Renormalization and Regularization Renormalization Group |
| title | On the resilience of the gravitational variational principle under renormalization |
| title_full | On the resilience of the gravitational variational principle under renormalization |
| title_fullStr | On the resilience of the gravitational variational principle under renormalization |
| title_full_unstemmed | On the resilience of the gravitational variational principle under renormalization |
| title_short | On the resilience of the gravitational variational principle under renormalization |
| title_sort | on the resilience of the gravitational variational principle under renormalization |
| topic | Classical Theories of Gravity Renormalization and Regularization Renormalization Group |
| url | https://doi.org/10.1007/JHEP10(2023)054 |
| work_keys_str_mv | AT giulioneri ontheresilienceofthegravitationalvariationalprincipleunderrenormalization AT stefanoliberati ontheresilienceofthegravitationalvariationalprincipleunderrenormalization |