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686
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 1474 (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.
Hierarchies from Fluxes in String Compactifications
, 2002
"... Warped compactifications with significant warping provide one of the few known mechanisms for naturally generating large hierarchies of physical scales. We demonstrate that this mechanism is realizable in string theory, and give examples involving orientifold compactifications of IIB string theory a ..."
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Cited by 724 (33 self)
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Warped compactifications with significant warping provide one of the few known mechanisms for naturally generating large hierarchies of physical scales. We demonstrate that this mechanism is realizable in string theory, and give examples involving orientifold compactifications of IIB string theory and Ftheory compactifications on CalabiYau fourfolds. In each case, the hierarchy of scales is fixed by a choice of RR and NS fluxes in the compact manifold. Our solutions involve compactifications of the KlebanovStrassler gravity dual to a confining N = 1 supersymmetric gauge theory, and the hierarchy reflects the small scale of chiral symmetry breaking in the dual gauge theory.
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 299 (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.
CFT’s from CalabiYau Fourfolds
 Nucl. Phys. B584
"... We consider F/M/Type IIA theory compactified to four, three, or two dimensions on a CalabiYau fourfold, and study the behavior near an isolated singularity in the presence of appropriate fluxes and branes. We analyze the vacuum and soliton structure of these models, and show that near an isolated ..."
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Cited by 277 (14 self)
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We consider F/M/Type IIA theory compactified to four, three, or two dimensions on a CalabiYau fourfold, and study the behavior near an isolated singularity in the presence of appropriate fluxes and branes. We analyze the vacuum and soliton structure of these models, and show that near an isolated singularity, one often generates massless chiral superfields and a superpotential, and in many instances in two or three dimensions one obtains nontrivial superconformal field theories. In the case of two dimensions, we identify some of these theories with certain KazamaSuzuki coset models, such as the N = 2 minimal models. June
Superstrings and topological strings at large
 N”, J. Math. Phys
"... We embed the large N ChernSimons/topological string duality in ordinary superstrings. This corresponds to a large N duality between generalized gauge systems with N = 1 supersymmetry in 4 dimensions and superstrings propagating on noncompact CalabiYau manifolds with certain fluxes turned on. We a ..."
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Cited by 258 (27 self)
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We embed the large N ChernSimons/topological string duality in ordinary superstrings. This corresponds to a large N duality between generalized gauge systems with N = 1 supersymmetry in 4 dimensions and superstrings propagating on noncompact CalabiYau manifolds with certain fluxes turned on. We also show that in a particular limit of the N = 1 gauge theory system, certain superpotential terms in the N = 1 system (including deformations if spacetime is noncommutative) are captured to all orders in 1/N by the amplitudes of noncritical bosonic strings propagating on a circle with selfdual radius. We also consider Dbrane/antiDbrane system wrapped over vanishing cycles of compact CalabiYau manifolds and argue that at large N they induce a shift in the background to a topologically distinct CalabiYau, which we identify as the ground state system of the Brane/antiBrane system. August
Toric Geometry, Sasaki–Einstein Manifolds and a new Infinite Class of AdS/CFT duals
"... Recently an infinite family of explicit Sasaki–Einstein metrics Y p,q on S 2 × S 3 has been discovered, where p and q are two coprime positive integers, with q < p. These give rise to a corresponding family of Calabi–Yau cones, which moreover are toric. Aided by several recent results in toric ge ..."
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Cited by 175 (15 self)
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Recently an infinite family of explicit Sasaki–Einstein metrics Y p,q on S 2 × S 3 has been discovered, where p and q are two coprime positive integers, with q < p. These give rise to a corresponding family of Calabi–Yau cones, which moreover are toric. Aided by several recent results in toric geometry, we show that these are Kähler quotients C 4 //U(1), namely the vacua of gauged linear sigma models with charges (p,p, −p + q, −p − q), thereby generalising the conifold, which is p = 1,q = 0. We present the corresponding toric diagrams and show that these may be embedded in the toric diagram for the orbifold C 3 /Zp+1 × Zp+1 for all q < p with fixed p. We hence find that the Y p,q manifolds are AdS/CFT dual to an infinite class of N = 1 superconformal field theories arising as infra–red (IR) fixed points of toric quiver gauge theories with gauge group SU(N) 2p. As a non–trivial example, we show that Y 2,1 is an explicit irregular Sasaki–Einstein metric on the horizon of the complex cone over the first del Pezzo surface. The dual quiver gauge theory has already been
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 164 (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
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 148 (27 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
Nekrasov, “Gravity duals of fractional branes and logarithmic
 RG flow,” Nucl. Phys. B
"... We study fractional branes in N = 2 orbifold and N = 1 conifold theories. Placing a large number N of regular D3branes at the singularity produces the dual AdS5 × X 5 geometry, and we describe the fractional branes as small perturbations to this background. For the orbifolds, X 5 = S 5 /Γ and fract ..."
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Cited by 140 (6 self)
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We study fractional branes in N = 2 orbifold and N = 1 conifold theories. Placing a large number N of regular D3branes at the singularity produces the dual AdS5 × X 5 geometry, and we describe the fractional branes as small perturbations to this background. For the orbifolds, X 5 = S 5 /Γ and fractional D3branes excite complex scalars from the twisted sector which are localized on the fixed circle of X 5. The resulting solutions are given by holomorphic functions and the fieldtheoretic betafunction is simply reproduced. For N regular and M fractional D3branes at the conifold singularity we find a nonconformal N = 1 supersymmetric SU(N + M) × SU(N) gauge theory. The dual Type IIB background is AdS5 × T 1,1 with NSNS and RR 2form fields turned on. This dual description reproduces the logarithmic flow of couplings found in the field theory. 11/99
The geometric dual of amaximisation for toric SasakiEinstein manifolds
, 2005
"... We show that the Reeb vector, and hence in particular the volume, of a Sasaki– Einstein metric on the base of a toric Calabi–Yau cone of complex dimension n may be computed by minimising a function Z on R n which depends only on the toric data that defines the singularity. In this way one can extrac ..."
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Cited by 133 (15 self)
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We show that the Reeb vector, and hence in particular the volume, of a Sasaki– Einstein metric on the base of a toric Calabi–Yau cone of complex dimension n may be computed by minimising a function Z on R n which depends only on the toric data that defines the singularity. In this way one can extract certain geometric information for a toric Sasaki–Einstein manifold without finding the metric explicitly. For complex dimension n = 3 the Reeb vector and the volume correspond to the R–symmetry and the a central charge of the AdS/CFT dual superconformal field theory, respectively. We therefore interpret this extremal problem as the geometric dual of a–maximisation. We illustrate our results with some examples, including the Y p,q singularities and the complex cone over the