TY - JOUR

T1 - Counterterms, Kounterterms, and the variational problem in AdS gravity

AU - Anastasiou, Giorgos

AU - Miskovic, Olivera

AU - Olea, Rodrigo

AU - Papadimitriou, Ioannis

PY - 2020/8/1

Y1 - 2020/8/1

N2 - 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.

AB - 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.

KW - AdS-CFT Correspondence

KW - Classical Theories of Gravity

KW - Gauge-gravity correspondence

KW - Renormalization Group

UR - http://www.scopus.com/inward/record.url?scp=85089586727&partnerID=8YFLogxK

U2 - 10.1007/JHEP08(2020)061

DO - 10.1007/JHEP08(2020)061

M3 - Article

AN - SCOPUS:85089586727

VL - 2020

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 8

M1 - 61

ER -