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Lecture notes on holographic renormalization
Open accessAbstract
We review the formalism of holographic renormalization. We start by discussing mathematical results on asymptotically anti-de Sitter (AdS) spacetimes. We then outline the general method of holographic renormalization. The method is illustrated by working all details in a simple example: a massive scalar field on anti-de Sitter spacetime. The discussion includes the derivation of the on-shell renormalized action, holographic Ward identities, anomalies and renormalization group (RG) equations, and the computation of renormalized one-, two- and four-point functions. We then discuss the application of the method to holographic RG flows. We also show that the results of the near-boundary analysis of asymptotically AdS spacetimes can be analytically continued to apply to asymptotically de Sitter spacetimes. In particular, it is shown that the Brown–York stress energy tensor of de Sitter spacetime is equal, up to a dimension-dependent sign, to the Brown–York stress energy tensor of an associated AdS spacetime.
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Cites
The large $N$ limit of superconformal field theories and supergravity
Maldacena, J. (1998) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.1998.v2.n2.a1 · Cited by 14,524
Anti de Sitter space and holography
Witten, E. (1998) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.1998.v2.n2.a2 · Cited by 13,070
Gauge theory correlators from non-critical string theory
Gubser, S. S., Klebanov, I. R., & Polyakov, A. M. (1998) · Physics Letters B · doi:10.1016/s0370-2693(98)00377-3 · Cited by 9,307
Gauge Theory Correlators from Non-Critical String Theory
Gubser, S. S., Klebanov, I. R., & Polyakov, A. M. (1998) · arXiv · doi:10.48550/arxiv.hep-th/9802109 · Cited by 9,307
The Large-N Limit of Superconformal Field Theories and Supergravity
Maldacena, J. (1999) · International Journal of Theoretical Physics · doi:10.1023/a:1026654312961 · Cited by 6,704
Quasilocal energy and conserved charges derived from the gravitational action
Brown, J. D., & York, J. W. (1993) · Physical Review D · doi:10.1103/physrevd.47.1407 · Cited by 1,793
A new proof of the positive energy theorem
Witten, E. (1981) · Communications in Mathematical Physics · doi:10.1007/bf01208277 · Cited by 1,595
Surface terms as counterterms in the AdS-CFT correspondence
Emparan, R., Johnson, C. V., & Myers, R. C. (1999) · Physical Review D · doi:10.1103/physrevd.60.104001 · Cited by 703
Cited by
Non-gaussian features of primordial fluctuations in single field inflationary models
Maldacena, J. (2003) · Journal of High Energy Physics · doi:10.1088/1126-6708/2003/05/013 · Cited by 2,906
Gravitation from entanglement in holographic CFTs
Faulkner, T., Guica, M., Hartman, T., Myers, R. C., & Van Raamsdonk, M. (2014) · Journal of High Energy Physics · doi:10.1007/jhep03(2014)051 · Cited by 520
Maldacena, J., & Maoz, L. (2004) · Journal of High Energy Physics · doi:10.1088/1126-6708/2004/02/053 · Cited by 426
Relative entropy and holography
Blanco, D. D., Casini, H., Hung, L.-Y., & Myers, R. C. (2013) · Journal of High Energy Physics · doi:10.1007/jhep08(2013)060 · Cited by 375
Comments on holographic complexity
Carmi, D., Myers, R. C., & Rath, P. (2017) · Journal of High Energy Physics · doi:10.1007/jhep03(2017)118 · Cited by 292
Metadata
- Authors
- Skenderis, K.
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2002-11-06
- Volume
- 19
- Issue
- 22
- Pages
- 5849-5876
- ISSN
- 0264-9381 (ISSN-L)
- OpenAlex
- W2153274301
- Cited by
- 1,427
- References
- 8
- FWCI
- 10.27
- Type
- journal article
- Language
- en
- Open access
- green
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