Results 1  10
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54
Large N field theories, string theory and gravity
, 2001
"... We review the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Antide Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evide ..."
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Cited by 1443 (45 self)
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We review the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Antide Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. We focus on the case of the N = 4 supersymmetric gauge theory in four dimensions, but we discuss also field theories in other dimensions, conformal and nonconformal, with or without supersymmetry, and in particular the relation to QCD. We also discuss some implications for black hole physics.
Operator product expansion of the lowest weight CPOs
 in N = 4 SYM(4) at strong coupling,” Nucl. Phys. B 586
, 2000
"... We present a detailed analysis of the 4point functions of the lowest weight chiral primary operators O I ∼ trφ (i φ j) in N = 4 SYM4 at strong coupling and show that their structure is compatible with the predictions of AdS/CFT correspondence. In particular, all powersingular terms in the 4point f ..."
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Cited by 69 (4 self)
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We present a detailed analysis of the 4point functions of the lowest weight chiral primary operators O I ∼ trφ (i φ j) in N = 4 SYM4 at strong coupling and show that their structure is compatible with the predictions of AdS/CFT correspondence. In particular, all powersingular terms in the 4point functions exactly coincide with the contributions coming from the conformal blocks of the CPOs, the Rsymmetry current and the stress tensor. Operators dual to string modes decouple at strong coupling. We compute the anomalous dimensions and the leading 1/N 2 corrections to the normalization constants of the 2 and 3point functions of scalar and vector doubletrace operators with approximate dimensions 4 and 5 respectively. We also find that the conformal dimensions of certain towers of doubletrace operators in the 105, 84 and 175 irreps are nonrenormalized. We show that, despite the absence of a nonrenormalization theorem for the doubletrace operator in the 20 irrep, its anomalous dimension vanishes. As byproducts of our investigation, we derive explicit expressions for the conformal block of the stress tensor, and for the conformal partial wave amplitudes of a conserved current and of a stress tensor in d dimensions. 1
Writing CFT correlation functions as AdS scattering amplitudes
"... We explore the Mellin representation of conformal correlation functions recently proposed by Mack. Examples in the AdS/CFT context reinforce the analogy between Mellin amplitudes and scattering amplitudes. We conjecture a simple formula relating the bulk scattering amplitudes to the asymptotic behav ..."
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Cited by 38 (5 self)
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We explore the Mellin representation of conformal correlation functions recently proposed by Mack. Examples in the AdS/CFT context reinforce the analogy between Mellin amplitudes and scattering amplitudes. We conjecture a simple formula relating the bulk scattering amplitudes to the asymptotic behavior of Mellin amplitudes and show that previous results on the flat space limit of AdS follow from our new formula. We find that the Mellin amplitudes are particularly useful in the case of conformal gauge theories in the planar limit. In this case, the four point Mellin amplitudes are meromorphic functions whose poles and their residues are entirely determined by two and three point functions of singletrace operators. This makes the Mellin amplitudes the ideal objects to attempt the conformal bootstrap program in higher dimensions. ar X iv
AdS(5) / CFT(4) four point functions of chiral primary operators: Cubic vertices
 Nucl. Phys. B
, 1999
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Constructing local bulk observables in interacting AdS/CFT,” Phys
 Rev. D
"... Local operators in the bulk of AdS can be represented as smeared operators in the dual CFT. We show how to construct these bulk observables by requiring that the bulk operators commute at spacelike separation. This extends our previous work by taking interactions into account. LargeN factorization ..."
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Cited by 14 (0 self)
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Local operators in the bulk of AdS can be represented as smeared operators in the dual CFT. We show how to construct these bulk observables by requiring that the bulk operators commute at spacelike separation. This extends our previous work by taking interactions into account. LargeN factorization plays a key role in the construction. We show diagrammatically how this procedure is related to bulk Feynman diagrams.
Aspects of the conformal Operator Product Expansion in AdS/CFT Correspondence
, 2000
"... We present a detailed analysis of a scalar conformal fourpoint function obtained from AdS/CFT correspondence. We study the scalar exchange graphs on AdSd+1 and discuss their analytic properties. Using methods of conformal partial wave analysis, we present a general procedure to study conformal four ..."
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Cited by 13 (3 self)
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We present a detailed analysis of a scalar conformal fourpoint function obtained from AdS/CFT correspondence. We study the scalar exchange graphs on AdSd+1 and discuss their analytic properties. Using methods of conformal partial wave analysis, we present a general procedure to study conformal fourpoint functions in terms of exchanges of scalar and tensor fields. The logarithmic terms in the fourpoint function are connected to the anomalous dimensions of the exchanged fields. Comparison of the results from AdSd+1 graphs with the conformal partial wave analysis suggests a possible general form for the operator product expansion of scalar fields in the boundary CFTd. 1
OPEs and 4point functions in AdS/CFT correspondence”, hepth/0002039. 24
 Aspects of the conformal Operator Product Expansion in AdS/CFT correspondence
"... Recently 4point correlation functions of axion and dilaton fields in type IIB SUGRA on AdS5 × S 5 were computed [1]. We reproduce from a CFT point of view all power law singular terms in these AdS 4point amplitudes. We also calculate a corresponding 4point function in the weak coupling limit, g2 ..."
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Cited by 7 (0 self)
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Recently 4point correlation functions of axion and dilaton fields in type IIB SUGRA on AdS5 × S 5 were computed [1]. We reproduce from a CFT point of view all power law singular terms in these AdS 4point amplitudes. We also calculate a corresponding 4point function in the weak coupling limit, g2 Y MN → 0. Comparison reveals the existence of a primary operator that contributes to these same singular terms in the weak coupling limit but which does not contribute to the power law singular terms of the type IIB SUGRA 4point functions. We conclude that this new operator is not a chiral primary and hence acquires a large anomalous dimension in the strong coupling regime. The AdS/CFT correspondence relates string theories on antide Sitter space (AdSd+1) backgrounds to ddimensional conformal field theories (CFTs) [2, 3, 4, 5]. One simple example of this correspondence, which is the only example
A Natural Language for AdS/CFT Correlators
"... We provide dramatic evidence that ‘Mellin space’ is the natural home for correlation functions in CFTs with weakly coupled bulk duals. In Mellin space, CFT correlators have poles corresponding to an OPE decomposition into ‘left ’ and ‘right’ subcorrelators, in direct analogy with the factorization ..."
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Cited by 4 (1 self)
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We provide dramatic evidence that ‘Mellin space’ is the natural home for correlation functions in CFTs with weakly coupled bulk duals. In Mellin space, CFT correlators have poles corresponding to an OPE decomposition into ‘left ’ and ‘right’ subcorrelators, in direct analogy with the factorization channels of scattering amplitudes. In the regime where these correlators can be computed by tree level Witten diagrams in AdS, we derive an explicit formula for the residues of Mellin amplitudes at the corresponding factorization poles, and we use the conformal Casimir to show that these amplitudes obey algebraic finite difference equations. By analyzing the recursive structure of our factorization formula we obtain simple diagrammatic rules for the construction of Mellin amplitudes corresponding to treelevel Witten diagrams in any bulk scalar theory. We prove the diagrammatic rules using our finite difference equations. Finally, we show that our factorization formula and our diagrammatic rules morph into the flat space SMatrix of the bulk theory, reproducing the usual Feynman rules, when we take the flat space limit of AdS/CFT. Throughout we emphasize a deep
Effective Conformal Theory and the FlatSpace Limit of AdS, arXiv:1007.2412
"... We develop the idea of an effective conformal theory describing the lowlying spectrum of the dilatation operator in a CFT. Such an effective theory is useful when the spectrum contains a hierarchy in the dimension of operators, and a small parameter whose role is similar to that of 1/N in a large ..."
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Cited by 2 (1 self)
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We develop the idea of an effective conformal theory describing the lowlying spectrum of the dilatation operator in a CFT. Such an effective theory is useful when the spectrum contains a hierarchy in the dimension of operators, and a small parameter whose role is similar to that of 1/N in a large N gauge theory. These criteria insure that there is a regime where the dilatation operator is modified perturbatively. Global AdS is the natural framework for perturbations of the dilatation operator respecting conformal invariance, much as Minkowski space naturally describes Lorentz invariant perturbations of the Hamiltonian. Assuming that the lowestdimension singletrace operator is a scalar, O, we consider the anomalous dimensions, γ(n, l), of the doubletrace operators of the form O(∂2)n(∂)lO. Purely from the CFT we find that perturbative unitarity places a bound on these dimensions of γ(n, l)  < 4. Nonrenormalizable AdS interactions lead to violations of the bound at large values of n. We also consider the case that these interactions are generated by integrating out a heavy scalar field in AdS. We show that the presence of the heavy field “unitarizes ” the growth in the anomalous dimensions, and leads to a resonancelike behavior in γ(n, l) when n is close to the dimension of the CFT operator dual to the heavy field. Finally, we demonstrate that bulk flatspace Smatrix elements can be extracted from the large n behavior of the anomalous dimensions. This leads to a direct connection between the spectrum of anomalous dimensions in ddimensional CFTs and flatspace Smatrix elements in d+ 1 dimensions. We comment on the emergence of flatspace locality from the CFT perspective. ar