论文标题
反应，kounterms和ADS重力中的变分问题
Counterterms, Kounterterms, and the variational problem in AdS gravity
论文作者
论文摘要
我们表明，当且仅当边界Weyl张量消失时，纯ADS重力的Kounterm均与通过全息重新归如此的边界对抗相吻合。特别是，kounterms仅在四个维度上仅在四个维度上造成了渐近近端广告的近端广告造成的变异问题。我们确定了共形扁平边界的对抗的确切形式，并证明，在范围内，Kounterms采取的形式完全相同。该协议可以理解为安德森定理的结构化量的同型紧凑型爱因斯坦4个manifolds及其较高维度的概括性，而Albin和Chang，Qing和Yang的较高维度概括。对于渐近尺寸的局部广告，具有共形扁平边界的歧管，Kounterms与边界对抗相一致，除了与全息形式的共形异常相关的对数差异和有限的局部项。
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.
