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On the renormalized volumes for conformally compact Einstein manifolds

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arxiv math/0512376 v2 pith:LEYZO3HL submitted 2005-12-15 math.DG math-phmath.MP

classification math.DGmath-phmath.MP
keywords renormalizedvolumecompactconformallyeinsteinanaloguechern-gauss-bonnetcome
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abstract

We study the renormalized volume of a conformally compact Einstein manifold. In even dimensions, we derive the analogue of the Chern-Gauss-Bonnet formula incorporating the renormalized volume. When the dimension is odd, we relate the renormalized volume to the conformal primitive of the $Q$-curvature. We show how all the global information come from the Scattering.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Conformal Renormalisation of 8D Einstein Gravity

    hep-th 2026-07 accept novelty 7.0 of 10

    Holographic renormalisation of 8D Einstein-AdS gravity is recovered as the Einstein sector of the unique conformal gravity admitting constant-negative-curvature Einstein solutions, with matching counterterms.

  2. Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs

    hep-th 2019-08 conditional novelty 6.0 of 10

    Kounterterm renormalization is extended to even-dimensional holographic CFTs, yielding a universal entanglement entropy formula whose logarithmic coefficient reproduces the type A central charge.

  3. On anomaly free 4d $\mathcal{N}$=4 and 6d (2,0) conformal supergravities and UV finiteness of Poincar\'e supergravities

    hep-th 2026-02 unverdicted novelty 4.0 of 10

    Anomaly cancellation for specific multiplet numbers in conformal supergravities implies divergences proportional to n_v+2 in 4d PSG and n_T-21 in 6d PSG.

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