Counterterms, Kounterterms, and the variational problem in AdS gravity

Giorgos Anastasiou, Olivera Miskovic, Rodrigo Olea, Ioannis Papadimitriou

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


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.

Original languageEnglish
Article number61
JournalJournal of High Energy Physics
Issue number8
StatePublished - 1 Aug 2020


  • AdS-CFT Correspondence
  • Classical Theories of Gravity
  • Gauge-gravity correspondence
  • Renormalization Group


Dive into the research topics of 'Counterterms, Kounterterms, and the variational problem in AdS gravity'. Together they form a unique fingerprint.

Cite this