Holographic Reconstruction of Spacetime¶and Renormalization in the AdS/CFT Correspondence

By S. de Haro, Kostas Skenderis, S. Solodukhin. 2000

1,658 citations recorded by the source corpus.

Abstract: We develop a systematic method for renormalizing the AdS/CFT prescription for computing correlation functions. This involves regularizing the bulk on-shell supergravity action in a covariant way, computing all divergences, adding counterterms to cancel them and then removing the regulator. We explicitly work out the case of pure gravity up to six dimensions and of gravity coupled to scalars. The method can also be viewed as providing a holographic reconstruction of the bulk spacetime metric and of bulk fields on this spacetime, out of conformal field theory data. Knowing which sources are turned on is sufficient in order to obtain an asymptotic expansion of the bulk metric and of bulk fields near the boundary to high enough order so that all infrared divergences of the on-shell action are obtained. To continue the holographic reconstruction of the bulk fields one needs new CFT data: the expectation value of the dual operator. In particular, in order to obtain the bulk metric one needs to know the expectation value of stress-energy tensor of the boundary theory. We provide completely explicit formulae for the holographic stress-energy tensors up to six dimensions. We show that both the gravitational and matter conformal anomalies of the boundary theory are correctly reproduced. We also obtain the conformal transformation properties of the boundary stress-energy tensors.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/13ed1b22238a3a786074de47706d218de7f0087f

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Citations in the corpus

Solid holography and massive gravity (2015, background): “the holographic renormalization [45]) it is desirable to have a covariant gravitational theory.”
Thermodynamics of Asymptotically Locally AdS Spacetimes (2005, methodology): “1) [16, 18, 25, 29].”
Complexity of formation in holography (2016, methodology): “es, e.g., see [29]. Hence to make sense of the calculation, we regulate with the standard approach of truncating the region on which the action is evaluated by a cuto surface at r= r max , see, e.g., [22,36,37].8 A potential subtlety here is that we wish to compare the WDW actions in the two dierent”
Comparison between various notions of conserved charges in asymptotically AdS spacetimes (2005, background): “We finally discuss and justify our boundary conditions by a linear perturbation analysis, and we comment on generalizations of our boundary conditions, as well as inclusion of matter fields.”
Quantum extremal islands made easy. Part I. Entanglement on the brane (2020, background): “, see [56, 63, 64].”
Relativistic Hydrodynamics in Heavy-Ion Collisions: General Aspects and Recent Developments (2016, background): “[129] S.”
Fake supergravity and domain wall stability (2003, background): “ﬃcients in (2.26) but g (d) are locally related to g (0). g (d) carries information about the vacuum and correlation functions of the dual QFT, so this coordinate system is well suited for holography [19]. Transforming the Janus solution to this coordinate system appears laborious and seems to lead ”
Holographic calculations of Rényi entropy (2011, background): “At this point, it is most systematic to work in the Fefferman-Graham (FG) gauge [44] — see also [45] — where the asymptotically AdS3 metric reads”
Holographic anatomy of fuzzballs (2006, background): “momentum is linear, the relation with the asymptotic coefficients is non-linear [ 24 ].”