en
2019-04-10T23:25
2001-03
http://link.springer.com/10.1007%2Fs002200100381
https://scigraph.springernature.com/explorer/license/
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.
595-622
research_article
articles
true
2001-03-01
Holographic Reconstruction of Spacetime¶and Renormalization in the AdS/CFT Correspondence
doi
10.1007/s002200100381
0010-3616
Communications in Mathematical Physics
1432-0916
Kostas
Skenderis
Mathematical Sciences
Physics Department, Princeton University, Princeton, NJ 08544, USA.¶E-mail: kostas¶feynman.princeton.edu, US
Princeton University
Sebastian
de Haro
dimensions_id
pub.1051944080
Pure Mathematics
readcube_id
f76e594519287e119f35ea09126035b1e7f573d60abff1bac39bac96d3ca6444
Sergey N.
Solodukhin
3
Spinoza Institute, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands.¶E-mail: haro@phys.uu.nl; S.Solodukhin@phys.uu.nl, NL
Utrecht University
Springer Nature - SN SciGraph project
217