Anti de sitter space and holography

Home
/
Papers
/
Anti de sitter space and holography

Posted Content•

Anti de sitter space and holography

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 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

Citations

PDF

Open Access

More filters

Journal Article•DOI•

Large N Field Theories, String Theory and Gravity

[...]

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.

...read moreread less

5,610 citations

Cites background or methods from "Anti de sitter space and holography..."

...4.1 Other AdS5 Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . ....
[...]
...28) from the point of view of the AdS theory [20]....
[...]
...If we consider a set of N coincident D-3-branes the near horizon geometry turns out to be AdS5 ×S5....
[...]
...So, we conclude that N = 4 U(N) Yang-Mills theory could be the same as ten dimensional superstring theory on AdS5 × S5 [5]....
[...]
...tions Extended supersymmetries in AdSp+2 with p = 2, 3, 4, 5 are classified by Nahm [92] (see also [111]) as AdS4 : OSp(N|4), N = 1, 2, · · · AdS5 : SU(2, 2|N /2), N = 2, 4, 6, 8 AdS6 : F (4) AdS7 : OSp(6, 2|N ), N = 2, 4....
[...]

Journal Article•DOI•

Holographic Derivation of Entanglement Entropy from the anti de Sitter Space/Conformal Field Theory Correspondence

[...]

Shinsei Ryu¹, Tadashi Takayanagi¹•Institutions (1)

Kavli Institute for Theoretical Physics¹

09 May 2006-Physical Review Letters

TL;DR: It is argued that the entanglement entropy in d + 1 dimensional conformal field theories can be obtained from the area of d dimensional minimal surfaces in AdS(d+2), analogous to the Bekenstein-Hawking formula for black hole entropy.

...read moreread less

Abstract: A holographic derivation of the entanglement entropy in quantum (conformal) field theories is proposed from anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We argue that the entanglement entropy in d + 1 dimensional conformal field theories can be obtained from the area of d dimensional minimal surfaces in AdS(d+2), analogous to the Bekenstein-Hawking formula for black hole entropy. We show that our proposal agrees perfectly with the entanglement entropy in 2D CFT when applied to AdS(3). We also compare the entropy computed in AdS(5)XS(5) with that of the free N=4 super Yang-Mills theory.

...read moreread less

4,395 citations

Journal Article•DOI•

Anti-de Sitter Space, Thermal Phase Transition, And Confinement in Gauge Theories

[...]

Edward Witten¹•Institutions (1)

Princeton University¹

16 Mar 1998-Advances in Theoretical and Mathematical Physics

TL;DR: The correspondence between supergravity and string theory on AdS space and boundary conformal eld theory relates the thermodynamics of N = 4 super Yang-Mills theory in four dimensions to the thermodynamic properties of Schwarzschild black holes in Anti-de Sitter space as mentioned in this paper.

...read moreread less

Abstract: The correspondence between supergravity (and string theory) on AdS space and boundary conformal eld theory relates the thermodynamics of N = 4 super Yang-Mills theory in four dimensions to the thermodynamics of Schwarzschild black holes in Anti-de Sitter space. In this description, quantum phenomena such as the spontaneous breaking of the center of the gauge group, magnetic connement, and the mass gap are coded in classical geometry. The correspondence makes it manifest that the entropy of a very large AdS Schwarzschild black hole must scale \holographically" with the volume of its horizon. By similar methods, one can also make a speculative proposal for the description of large N gauge theories in four dimensions without supersymmetry.

...read moreread less

4,209 citations

Cites background or methods from "Anti de sitter space and holography..."

...In [27,47], a precise recipe was presented for computing CFT observables in terms of...
[...]
...However, a variety of arguments [47] show that the AdS theory encodes a SU(N) gauge group, not U(N)....
[...]
...The version of the CFT/AdS correspondence that we will use asserts that conformal field theory on an n-manifold M is to be studied by summing over contributions of Einstein manifolds B of dimension n+ 1 which (in a sense explained in [27,47]) have M at infinity....
[...]
...2 of [47], is to understand the high temperature behavior of N = 4 super Yang-Mills theory....
[...]
...We could do this by analyzing correlation functions, using the formulation of [27,47], but it is more direct to use a Hamiltonian approach (discussed at the end of [47]) in which one identifies the quantum states of the supergravity theory with those of the quantum field theory on the boundary....
[...]

Journal Article•DOI•

Non-Gaussian features of primordial fluctuations in single field inflationary models

[...]

Juan Maldacena¹•Institutions (1)

Institute for Advanced Study¹

10 May 2003-Journal of High Energy Physics

TL;DR: In this article, the three point correlation functions for primordial scalar and tensor fluctuations in single field inflationary models were computed in the slow roll limit, where the answer is given terms of the two usual slow roll parameters.

...read moreread less

Abstract: We compute the three point correlation functions for primordial scalar and tensor fluctuations in single field inflationary models We obtain explicit expressions in the slow roll limit where the answer is given terms of the two usual slow roll parameters In a particular limit the three point functions are determined completely by the tilt of the spectrum of the two point functions We also make some remarks on the relation of this computation to dS/CFT and AdS/CFT We emphasize that (A)dS/CFT can be viewed as a statement about the wavefunction of the universe

...read moreread less

3,153 citations

Journal Article•DOI•

Viscosity in strongly interacting quantum field theories from black hole physics

[...]

Pavel Kovtun¹, Dan T. Son², Andrei O. Starinets³•Institutions (3)

Kavli Institute for Theoretical Physics¹, University of Washington², Perimeter Institute for Theoretical Physics³

22 Mar 2005-Physical Review Letters

TL;DR: It is provided evidence that this value of shear viscosity to volume density of entropy may serve as a lower bound for a wide class of systems, thus suggesting that black hole horizons are dual to the most ideal fluids.

...read moreread less

Abstract: The ratio of shear viscosity to volume density of entropy can be used to characterize how close a given fluid is to being perfect. Using string theory methods, we show that this ratio is equal to a universal value of [h-bar]/4pikB for a large class of strongly interacting quantum field theories whose dual description involves black holes in anti–de Sitter space. We provide evidence that this value may serve as a lower bound for a wide class of systems, thus suggesting that black hole horizons are dual to the most ideal fluids.

...read moreread less

2,721 citations

Cites background from "Anti de sitter space and holography..."

...] One can have in mind, as an example, the near-extremal D3-brane in type IIB supergravity, dual to finite-temperature N = 4 supersymmetric SU(Nc) Yang–Mills theory in the limit of large Nc and large ’t Hooft coupling [7, 8, 9, 10], ds(2) = r(2) R2 [...
[...]

1
2
3
4
…
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200

Collapse

References

PDF

Open Access

More filters

Journal Article•DOI•

The Large N limit of superconformal field theories and supergravity

[...]

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.

...read moreread less

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.

...read moreread less

15,567 citations

Journal Article•DOI•

Gauge Theory Correlators from Non-Critical String Theory

[...]

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.

...read moreread less

11,887 citations

"Anti de sitter space and holography..." refers background in this paper

...After this work was substantially completed, I learned of independent work [36] in which a very similar understanding of the the CFT/AdS correspondence to what we describe in section 2 is developed, as well as two papers [37,38] that consider facts relevant to or aspects of the Hamiltonian formalism that we consider in section 3....
[...]

Book•

The Large Scale Structure of Space-Time

[...]

Stephen W. Hawking, George F. R. Ellis

01 Jan 1973

TL;DR: In this paper, the authors discuss the General Theory of Relativity in the large and discuss the significance of space-time curvature and the global properties of a number of exact solutions of Einstein's field equations.

...read moreread less

Abstract: Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a 'black hole' in space; and secondly, that there will exist singularities in space-time itself. These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. A discussion of the Cauchy problem for General Relativity is also included in this 1973 book.

...read moreread less

8,932 citations

Journal Article•DOI•

Quantum field theory and the Jones polynomial

[...]

Edward Witten¹•Institutions (1)

Institute for Advanced Study¹

01 Sep 1989-Communications in Mathematical Physics

TL;DR: In this paper, it was shown that 2+1 dimensional quantum Yang-Mills theory with an action consisting purely of the Chern-Simons term is exactly soluble and gave a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms.

...read moreread less

Abstract: It is shown that 2+1 dimensional quantum Yang-Mills theory, with an action consisting purely of the Chern-Simons term, is exactly soluble and gives a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms. In this version, the Jones polynomial can be generalized fromS 3 to arbitrary three manifolds, giving invariants of three manifolds that are computable from a surgery presentation. These results shed a surprising new light on conformal field theory in 1+1 dimensions.

...read moreread less

5,093 citations

"Anti de sitter space and holography..." refers methods in this paper

...The realization of holography via AdS space is also reminiscent of the relation [35] between conformal field theory in two dimensions and Chern-Simons gauge theory in three dimensions....
[...]

Journal Article•DOI•

A planar diagram theory for strong interactions

[...]

Gerard 't Hooft¹•Institutions (1)

CERN¹

18 Apr 1974-Nuclear Physics

TL;DR: In this article, it was shown that only planar diagrams with the quarks at the edges dominate; the topological structure of the perturbation series in 1/N is identical to that of the dual models, such that the number 1/n corresponds to the dual coupling constant.

...read moreread less

4,449 citations

"Anti de sitter space and holography..." refers background in this paper

...In large N QCD, such behavior cannot prevail at all temperatures....
[...]
...It is surprising that this comparison will work, since QCD is confining, while the N = 4 theory has no obviously analogous phenomenon....
[...]
...The whole idea of the 1/N expansion as an approach to QCD [1] is that for large N , the Hilbert space of the theory consists of color singlet particles whose masses and...
[...]
...The whole idea of the 1/N expansion as an approach to QCD [1] is that for large N , the Hilbert space of the theory consists of color singlet particles whose masses and multiplicities are independent of N ....
[...]
...We will therefore compare to the expected large N thermodynamics [57] of an SU(N) gauge theory with massive quarks in the fundamental representation (that is, ordinary QCD generalized to large N)....
[...]