Counterterms, Kounterterms, and the variational problem in AdS gravity
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Fecha
2020-08
Profesor/a Guía
Facultad/escuela
Idioma
en
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Editor
Springer
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Licencia CC
Attribution 4.0 International (CC BY 4.0)
Licencia CC
https://creativecommons.org/licenses/by/4.0/
Resumen
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. © 2020, The Author(s).
Notas
Indexación: Scopus.
Palabras clave
AdS-CFT Correspondence, Classical Theories of Gravity, Gauge-gravity correspondence, Renormalization Group
Citación
Journal of High Energy Physics Open Access Volume 2020, Issue 81 August 2020 Article number 61
DOI
10.1007/JHEP08(2020)061