A Stress tensor for Anti-de Sitter gravity

doi:10.1007/S002200050764

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A Stress tensor for Anti-de Sitter gravity

Journal Article•DOI•

A Stress tensor for Anti-de Sitter gravity

Vijay Balasubramanian¹, Per Kraus²•Institutions (2)

Harvard University¹, University of Chicago²

17 Feb 1999-Communications in Mathematical Physics (Springer-Verlag)-Vol. 208, Iss: 2, pp 413-428

TL;DR: In this paper, the boundary stress tensor associated with a gravitating system in asymptotically anti-de Sitter space is computed, and the conformal anomalies in two and four dimensions are recovered.

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Abstract: We propose a procedure for computing the boundary stress tensor associated with a gravitating system in asymptotically anti-de Sitter space. Our definition is free of ambiguities encountered by previous attempts, and correctly reproduces the masses and angular momenta of various spacetimes. Via the AdS/CFT correspondence, our classical result is interpretable as the expectation value of the stress tensor in a quantum conformal field theory. We demonstrate that the conformal anomalies in two and four dimensions are recovered. The two dimensional stress tensor transforms with a Schwarzian derivative and the expected central charge. We also find a nonzero ground state energy for global AdS5, and show that it exactly matches the Casimir energy of the dual super Yang–Mills theory on S 3×R.

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Journal Article•DOI•

Large N Field Theories, String Theory and Gravity

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Ofer Aharony¹, Steven S. Gubser², Juan Maldacena², Hirosi Ooguri³, Hirosi Ooguri⁴, Yaron Oz⁵ - Show less +2 more•Institutions (5)

Rutgers University¹, Harvard University², University of California, Berkeley³, Lawrence Berkeley National Laboratory⁴, CERN⁵

01 Jan 2000-Physics Reports

TL;DR: In this paper, the holographic correspondence between field theories and string/M theory is discussed, focusing on the relation between compactifications of string theory on anti-de Sitter spaces and conformal field theories.

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5,610 citations

Cites background from "A Stress tensor for Anti-de Sitter ..."

...This was indeed found to be true in [226, 227, 228, 229](5), where the conformal anomaly was shown to arise from subtleties in the regularization of the (divergent) supergravity action on AdS space....
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...The result of [226, 227, 228, 229] implies that a computation using gravity on AdS5 always gives rise to theories with (5)A generalization with more varying fields may be found in [230]....
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Journal Article•DOI•

Aspects of Holographic Entanglement Entropy

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Shinsei Ryu¹, Tadashi Takayanagi²•Institutions (2)

Kavli Institute for Theoretical Physics¹, Kyoto University²

21 Aug 2006-Journal of High Energy Physics

TL;DR: In this paper, a holographic interpretation of entanglement entropy in conformal field theories is proposed from AdS/CFT correspondence, and the relation between the entropy and central charges in 4D conformal fields is examined.

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Abstract: This is an extended version of our short report [1], where a holographic interpretation of entanglement entropy in conformal field theories is proposed from AdS/CFT correspondence. In addition to a concise review of relevant recent progresses of entanglement entropy and details omitted in the earlier letter, this paper includes the following several new results: We give a more direct derivation of our claim which relates the entanglement entropy with the minimal area surfaces in the AdS3/CFT2 case as well as some further discussions on higher dimensional cases. Also the relation between the entanglement entropy and central charges in 4D conformal field theories is examined. We check that the logarithmic part of the 4D entanglement entropy computed in the CFT side agrees with the AdS5 result at least under a specific condition. Finally we estimate the entanglement entropy of massive theories in generic dimensions by making use of our proposal.

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2,310 citations

Journal Article•DOI•

Lectures on holographic methods for condensed matter physics

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Sean A. Hartnoll¹•Institutions (1)

Harvard University¹

21 Nov 2009-Classical and Quantum Gravity

TL;DR: In this article, a discussion of holographic techniques progresses from equilibrium, to transport and to superconductivity, and the discussion of supergravity, Strings and Gauge theories are discussed.

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Abstract: These notes are loosely based on lectures given at the CERN Winter School on Supergravity, Strings and Gauge theories, February 2009, and at the IPM String School in Tehran, April 2009. I have focused on a few concrete topics and also on addressing questions that have arisen repeatedly. Background condensed matter physics material is included as motivation and easy reference for the high energy physics community. The discussion of holographic techniques progresses from equilibrium, to transport and to superconductivity.

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1,951 citations

Additional excerpts

...[50, 51]) SE = − 1 2κ2 ∫ dx √ g ( R+ d(d− 1) L2 ) + 1 2κ2 ∫...
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Journal Article•DOI•

Holographic reconstruction of spacetime and renormalization in the AdS/CFT correspondence

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Sebastian de Haro¹, Kostas Skenderis², Sergey N. Solodukhin¹•Institutions (2)

Utrecht University¹, Princeton University²

01 Mar 2001-Communications in Mathematical Physics

TL;DR: In this paper, the authors developed a method for renormalizing the AdS/CFT prescription for computing correlation functions, which 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.

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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.

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1,795 citations

Cites background or methods from "A Stress tensor for Anti-de Sitter ..."

...22) As we have remark before, 〈Tij〉 has a dual meaning [7], both as the expectation value of the dual stressenergy tensor and as the quasi-local stress-energy tensor of Brown and York....
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...In particular, in the case the operator is the stess energy tensor, our formulae have a “dual” meaning [7]: both as the expectation value of the stress-energy tensor of the dual CFT and as the quasi-local stress-energy tensor of Brown and York [15]....
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...It was pointed out in [7] that this prescription for calculating the boundary stress-energy tensor provides also a novel, free of divergences(5), way of computing the gravitational quasi-local stress-energy tensor of Brown and York [15]....
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...Minimally subtracting the divergences by adding counterterms [11] leads straightforwardly to the results in [7, 9, 10]....
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...These are exactly the counterterms in [7, 9, 10] except that these authors did not include the logarithmic divergence....
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Journal Article•DOI•

Ads/CFT correspondence and symmetry breaking

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Igor R. Klebanov¹, Edward Witten¹•Institutions (1)

Princeton University¹

06 Sep 1999-Nuclear Physics

TL;DR: In this paper, the authors study the vacua of field theories where some of the gauge symmetry is broken by expectation values of scalar fields, and show how to calculate them from the behavior of perturbations to the AdS background near the boundary.

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1,674 citations

Cites methods or result from "A Stress tensor for Anti-de Sitter ..."

...Up to normalization this is the same relation as the one advocated in [16,17,14,18,19]....
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...We also formulate, following similar ideas in [16,17,14,18,19], the general procedure for computing the expectation value of an operator in a quantum vacuum that is related to a given classical solution....
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References

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Journal Article•DOI•

The Large N limit of superconformal field theories and supergravity

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Juan Maldacena¹•Institutions (1)

Harvard University¹

01 Jan 1998-Advances in Theoretical and Mathematical Physics

TL;DR: In this article, it was shown that the large-N limits of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravityon the product of anti-de Sitter spacetimes, spheres, and other compact manifolds.

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Abstract: We show that the large-N limits of certainconformal field theories in various dimensions includein their Hilbert space a sector describing supergravityon the product of anti-de Sitter spacetimes, spheres, and other compact manifolds. This is shown bytaking some branes in the full M/string theory and thentaking a low-energy limit where the field theory on thebrane decouples from the bulk. We observe that, in this limit, we can still trust thenear-horizon geometry for large N. The enhancedsupersymmetries of the near-horizon geometry correspondto the extra supersymmetry generators present in thesuperconformal group (as opposed to just the super-Poincaregroup). The 't Hooft limit of 3 + 1 N = 4 super-Yang–Mills at the conformal pointis shown to contain strings: they are IIB strings. Weconjecture that compactifications of M/string theory on various anti-de Sitterspacetimes is dual to various conformal field theories.This leads to a new proposal for a definition ofM-theory which could be extended to include fivenoncompact dimensions.

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15,567 citations

Journal Article•DOI•

Anti De Sitter Space And Holography

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Edward Witten

20 Feb 1998-Advances in Theoretical and Mathematical Physics

TL;DR: In this article, it was shown that the Kaluza-Klein modes of Type IIB supergravity on $AdS_5\times {\bf S}^5$ match with the chiral operators of the super Yang-Mills theory in four dimensions.

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Abstract: Recently, it has been proposed by Maldacena that large $N$ limits of certain conformal field theories in $d$ dimensions can be described in terms of supergravity (and string theory) on the product of $d+1$-dimensional $AdS$ space with a compact manifold. Here we elaborate on this idea and propose a precise correspondence between conformal field theory observables and those of supergravity: correlation functions in conformal field theory are given by the dependence of the supergravity action on the asymptotic behavior at infinity. In particular, dimensions of operators in conformal field theory are given by masses of particles in supergravity. As quantitative confirmation of this correspondence, we note that the Kaluza-Klein modes of Type IIB supergravity on $AdS_5\times {\bf S}^5$ match with the chiral operators of ${\cal N}=4$ super Yang-Mills theory in four dimensions. With some further assumptions, one can deduce a Hamiltonian version of the correspondence and show that the ${\cal N}=4$ theory has a large $N$ phase transition related to the thermodynamics of $AdS$ black holes.

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14,084 citations

Journal Article•DOI•

Gauge Theory Correlators from Non-Critical String Theory

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Steven S. Gubser¹, Igor R. Klebanov¹, Alexander M. Polyakov¹•Institutions (1)

Princeton University¹

28 May 1998-Physics Letters B

TL;DR: In this paper, a boundary of the anti-deSitter space analogous to a cut-off on the Liouville coordinate of the two-dimensional string theory is introduced to obtain certain Green's functions in 3+1-dimensional N = 4 supersymmetric Yang-Mills theory with a large number of colors via non-critical string theory.

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11,887 citations

"A Stress tensor for Anti-de Sitter ..." refers background in this paper

... been proposed which equates the gravitational action of the bulk viewed as a functional of boundary data, with the quantum eﬀective action of a conformal ﬁeld theory (CFT) deﬁned on the AdS boundary [2, 3, 4]. According to this correspondence, (1) can be interpreted as giving the expectation value of the stress tensor in the CFT:1 hTµνi = 2 √ −γ δSeﬀ δγµν . (2) The divergences which appear as the boundary...
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Posted Content•

Anti de sitter space and holography

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Edward Witten

20 Feb 1998-arXiv: High Energy Physics - Theory

TL;DR: In this article, a correspondence between conformal field theory observables and those of supergravity was proposed, where correlation functions in conformal fields are given by the dependence of the supergravity action on the asymptotic behavior at infinity.

...read moreread less

Abstract: Recently, it has been proposed by Maldacena that large $N$ limits of certain conformal field theories in $d$ dimensions can be described in terms of supergravity (and string theory) on the product of $d+1$-dimensional $AdS$ space with a compact manifold. Here we elaborate on this idea and propose a precise correspondence between conformal field theory observables and those of supergravity: correlation functions in conformal field theory are given by the dependence of the supergravity action on the asymptotic behavior at infinity. In particular, dimensions of operators in conformal field theory are given by masses of particles in supergravity. As quantitative confirmation of this correspondence, we note that the Kaluza-Klein modes of Type IIB supergravity on $AdS_5\times {\bf S}^5$ match with the chiral operators of $\N=4$ super Yang-Mills theory in four dimensions. With some further assumptions, one can deduce a Hamiltonian version of the correspondence and show that the $\N=4$ theory has a large $N$ phase transition related to the thermodynamics of $AdS$ black holes.

...read moreread less

8,751 citations

"A Stress tensor for Anti-de Sitter ..." refers methods in this paper

...This interpretation of divergences was first discussed in [4], and has been applied to various computations in, e....
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...The mechanism for obtaining a conformal anomaly from the AdS/CFT correspondence was outlined by Witten [4] and studied in detail by Henningson and Skenderis [8]....
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...A duality has been proposed which equates the gravitational action of the bulk viewed as a functional of boundary data, with the quantum effective action of a conformal field theory (CFT) defined on the AdS boundary [2, 3, 4]....
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