Results 1  10
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163
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.
Renormalization group flows from holography  Supersymmetry and a ctheorem
 ADV THEOR. MATH. PHYS
, 1999
"... We obtain first order equations that determine a supersymmetric kink solution in fivedimensional N = 8 gauged supergravity. The kink interpolates between an exterior antide Sitter region with maximal supersymmetry and an interior antide Sitter region with one quarter of the maximal supersymmetry. ..."
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Cited by 294 (25 self)
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We obtain first order equations that determine a supersymmetric kink solution in fivedimensional N = 8 gauged supergravity. The kink interpolates between an exterior antide Sitter region with maximal supersymmetry and an interior antide Sitter region with one quarter of the maximal supersymmetry. One eighth of supersymmetry is preserved by the kink as a whole. We interpret it as describing the renormalization group flow in N = 4 superYangMills theory broken to an N = 1 theory by the addition of a mass term for one of the three adjoint chiral superfields. A detailed correspondence is obtained between fields of bulk supergravity in the interior antide Sitter region and composite operators of the infrared field theory. We also point out that the truncation used to find the reduced symmetry critical point can be extended to obtain a new N = 4 gauged supergravity theory holographically dual to a sector of N = 2 gauge theories based on quiver diagrams. We consider more general kink geometries and construct a cfunction that is positive and monotonic if a weak energy condition holds in the bulk gravity theory. For evendimensional boundaries, the cfunction coincides with the trace anomaly coefficients of the holographically related field theory in limits where conformal invariance is recovered.
An infinite family of superconformal quiver gauge theories with SasakiEinstein duals
 JHEP
, 2005
"... Abstract: We describe an infinite family of quiver gauge theories that are AdS/CFT dual to a corresponding class of explicit horizon Sasaki–Einstein manifolds. The quivers may be obtained from a family of orbifold theories by a simple iterative procedure. A key aspect in their construction relies on ..."
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Cited by 158 (33 self)
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Abstract: We describe an infinite family of quiver gauge theories that are AdS/CFT dual to a corresponding class of explicit horizon Sasaki–Einstein manifolds. The quivers may be obtained from a family of orbifold theories by a simple iterative procedure. A key aspect in their construction relies on the global symmetry which is dual to the isometry of the manifolds. For an arbitrary such quiver we compute the exact R–charges of the fields in the IR by applying a–maximization. The values we obtain are generically quadratic irrational numbers and agree perfectly with the central charges and baryon charges computed from the family of metrics using the AdS/CFT correspondence. These results open the way for a systematic study of the quiver gauge theories and their dual geometries. Contents
The exact superconformal Rsymmetry maximizes a,” Nucl. Phys
 Sahakyan, “Central charges and U(1)R symmetries in N = 1 super Yang Mills,” JHEP 11 (2003) 013, hepth/0308071
"... An exact and general solution is presented for a previously open problem. We show that the superconformal Rsymmetry of any 4d SCFT is exactly and uniquely determined by a maximization principle: it is the Rsymmetry, among all possibilities, which (locally) maximizes the combination of ’t Hooft ano ..."
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Cited by 153 (15 self)
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An exact and general solution is presented for a previously open problem. We show that the superconformal Rsymmetry of any 4d SCFT is exactly and uniquely determined by a maximization principle: it is the Rsymmetry, among all possibilities, which (locally) maximizes the combination of ’t Hooft anomalies atrial(R) ≡ (9TrR3 − 3TrR)/32. The maximal value of atrial is then, by a result of Anselmi et. al., the central charge a of the SCFT. Our atrial maximization principle almost immediately ensures that the central charge a decreases upon any RG flow, since relevant deformations force atrial to be maximized over a subset of the previously possible Rsymmetries. Using atrial maximization, we find the exact superconformal Rsymmetry (and thus the exact anomalous dimensions of all chiral operators) in a variety of previously mysterious 4d N = 1 SCFTs. As a check, we verify that our exact results reproduce the perturbative anomalous dimensions in all perturbatively accessible RG fixed points. April
Gauge theories from toric geometry and brane tilings
, 2005
"... We provide a general set of rules for extracting the data defining a quiver gauge theory from a given toric Calabi–Yau singularity. Our method combines information from the geometry and topology of Sasaki–Einstein manifolds, AdS/CFT, dimers, and brane tilings. We explain how the field content, quan ..."
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Cited by 147 (25 self)
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We provide a general set of rules for extracting the data defining a quiver gauge theory from a given toric Calabi–Yau singularity. Our method combines information from the geometry and topology of Sasaki–Einstein manifolds, AdS/CFT, dimers, and brane tilings. We explain how the field content, quantum numbers, and superpotential of a superconformal gauge theory on D3–branes probing a toric Calabi–Yau singularity can be deduced. The infinite family of toric singularities with known horizon Sasaki–Einstein manifolds La,b,c is used to illustrate these ideas. We construct the corresponding quiver gauge theories, which may be fully specified by giving a tiling of the plane by hexagons with certain gluing rules. As checks of this construction, we perform amaximisation as well as Zminimisation to compute the exact Rcharges of an arbitrary such quiver. We also examine a number of examples in detail, including the infinite subfamily La,b,a, whose smallest member is the
Aspects of Holographic Entanglement Entropy
"... This is an extended version of our short report hepth/0603001, 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 ..."
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Cited by 126 (4 self)
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This is an extended version of our short report hepth/0603001, 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.
Toric Duality Is Seiberg Duality
, 2001
"... We study four N = 1 SU(N) 6 gauge theories, with bifundamental chiral matter and a superpotential. In the infrared, these gauge theories all realize the lowenergy worldvolume description of N coincident D3branes transverse to the complex cone over a del Pezzo surface dP3 which is the blowup of P2 ..."
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Cited by 79 (0 self)
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We study four N = 1 SU(N) 6 gauge theories, with bifundamental chiral matter and a superpotential. In the infrared, these gauge theories all realize the lowenergy worldvolume description of N coincident D3branes transverse to the complex cone over a del Pezzo surface dP3 which is the blowup of P2 at three generic points. Therefore, the four gauge theories are expected to fall into the same universality classâan example of a phenomenon that has been termed âtoric duality.â However, little independent evidence has been given that such theories are infraredequivalent. In fact, we show that the four gauge theories are related by the N = 1 duality of Seiberg, vindicating this expectation. We also study holographic aspects of these gauge theories. In particular we relate the spectrum of chiral operators in the gauge theories to wrapped D3brane states in the AdS dual description. We finally demonstrate that the other known examples of toric duality are related by N = 1 duality, a fact which we conjecture holds generally.
Positivity constraints on anomalies in supersymmetric gauge theories”, Phys
 Rev. D57
, 1998
"... The relation between the trace and Rcurrent anomalies in supersymmetric theories implies that the U(1)RF 2, U(1)R and U(1) 3 R anomalies which are matched in studies of N = 1 Seiberg duality satisfy positivity constraints. Some constraints are rigorous and others conjectured as fourdimensional gen ..."
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Cited by 69 (7 self)
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The relation between the trace and Rcurrent anomalies in supersymmetric theories implies that the U(1)RF 2, U(1)R and U(1) 3 R anomalies which are matched in studies of N = 1 Seiberg duality satisfy positivity constraints. Some constraints are rigorous and others conjectured as fourdimensional generalizations of the Zamolodchikov ctheorem. These constraints are tested in a large number of N = 1 supersymmetric gauge theories in the nonAbelian Coulomb phase, and they are satisfied in all renormalizable models with unique anomalyfree Rcurrent, including those with accidental symmetry. Most striking is the fact that the flow of the Euler anomaly coefficient, aUV − aIR, is always positive, as conjectured by Cardy. 1 1