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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 Anti-de 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 Anti-de 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 non-conformal, with or without supersymmetry, and in particular the relation to QCD. We also discuss some implications for black hole physics.
Anti-de Sitter Space, Thermal Phase Transition, and Confinement in Gauge Theories
- Adv. Theor. Math. Phys
, 1998
"... The correspondence between supergravity (and string theory) on AdS space and boundary conformal field 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 phenome ..."
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Cited by 1087 (4 self)
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The correspondence between supergravity (and string theory) on AdS space and boundary conformal field 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 confinement, 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. March
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 F-theory compactifications on Calabi-Yau four-folds. 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 Klebanov-Strassler 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.
Superconformal field theory on threebranes at a Calabi-Yau singularity
- Nucl. Phys. B
, 1998
"... Just as parallel threebranes on a smooth manifold are related to string theory on AdS5 × S 5, parallel threebranes near a conical singularity are related to string theory on AdS5 × X5, for a suitable X5. For the example of the conifold singularity, for which X5 = (SU(2) × SU(2))/U(1), we argue that ..."
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Cited by 690 (37 self)
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Just as parallel threebranes on a smooth manifold are related to string theory on AdS5 × S 5, parallel threebranes near a conical singularity are related to string theory on AdS5 × X5, for a suitable X5. For the example of the conifold singularity, for which X5 = (SU(2) × SU(2))/U(1), we argue that string theory on AdS5 × X5 can be described by a certain N = 1 supersymmetric gauge theory which we describe in detail.
Macroscopic strings as heavy quarks in large N gauge theory and Anti-de Sitter supergravity
- PHYS. J. C22
"... Maldacena has put forward large N correspondence between superconformal field theories on the brane and anti-de Sitter supergravity in spacetime. We study some aspects of the correspondence between N = 4 superconformal gauge theory on D3-brane and maximal supergravity on adS5 × S5 by introducing mac ..."
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Cited by 510 (1 self)
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Maldacena has put forward large N correspondence between superconformal field theories on the brane and anti-de Sitter supergravity in spacetime. We study some aspects of the correspondence between N = 4 superconformal gauge theory on D3-brane and maximal supergravity on adS5 × S5 by introducing macroscopic strings as heavy (anti)-quark probes. The macroscopic strings are semi-infinite Type IIB strings ending on D3-brane world-volume. We first study deformation and fluctuation of D3-brane when a macroscopic BPS string is attached. We find that both dynamics and boundary conditions agree with those for macroscopic string in anti-de Sitter supergravity. As a by-product we clarify how Polchinski’s Dirichlet and Neumann open string boundary conditions arise. We then study non-BPS macroscopic string anti-string pair configuration as physical realization of heavy quark Wilson loop. We obtain Q ¯ Q static potential and again find agreements between the gauge theory and the supergravity results. By turning on Ramond-Ramond zero-form potential, we also study θ vacuum angle dependence of the static potential. We finally discuss dynamical realization of loop equation via turning on local electric field and recoil of heavy quark thereof, and of heavy baryon via of N-prong string junction. Throughout comparisons of the correspondence, we emphasize crucial role played by ‘geometric duality ’ between coordinates perpendicular to D3-brane and parallel ones, hinting a possible explanation of emergence of the entire adS5 spacetime.
Supergravity and the large N limit of theories with sixteen supercharges
, 1998
"... We consider field theories with sixteen supersymmetries, which includes U(N) Yang-Mills theories in various dimensions, and argue that their large N limit is related to certain supergravity solutions. We study this by considering a system of D-branes in string theory and then taking a limit where th ..."
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Cited by 391 (14 self)
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We consider field theories with sixteen supersymmetries, which includes U(N) Yang-Mills theories in various dimensions, and argue that their large N limit is related to certain supergravity solutions. We study this by considering a system of D-branes in string theory and then taking a limit where the brane worldvolume theory decouples from gravity. At the same time we study the corresponding D-brane supergravity solution and argue that we can trust it in certain regions where the curvature (and the effective string coupling, where appropriate) are small. The supergravity solutions typically have several weakly coupled regions and interpolate between different limits of string-M-theory.
Perturbative gauge theory as a string theory in twistor space
- Commun. Math. Phys
"... Perturbative scattering amplitudes in Yang-Mills theory have many unexpected properties, such as holomorphy of the maximally helicity violating amplitudes. To interpret these results, we Fourier transform the scattering amplitudes from momentum space to twistor space, and argue that the transformed ..."
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Cited by 388 (0 self)
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Perturbative scattering amplitudes in Yang-Mills theory have many unexpected properties, such as holomorphy of the maximally helicity violating amplitudes. To interpret these results, we Fourier transform the scattering amplitudes from momentum space to twistor space, and argue that the transformed amplitudes are supported on certain holomorphic curves. This in turn is apparently a consequence of an equivalence between the perturbative expansion of N = 4 super Yang-Mills theory and the D-instanton expansion of a certain string theory, namely the topological B model whose target space is the Calabi-Yau supermanifold CP 3|4. December
Mirror Manifolds and Topological Field Theory
- in Essays on Mirror Manifolds (ed. S.T. Yau), International Press, Hong Kong
, 1992
"... In N = 4 super Yang-Mills theory on a four-manifold M, one can specify a discrete magnetic flux valued in H2 (M,ZN). This flux is encoded in the AdS/CFT correspondence in terms of a five-dimensional topological field theory with Chern-Simons action. A similar topological field theory in seven dimens ..."
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Cited by 385 (14 self)
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In N = 4 super Yang-Mills theory on a four-manifold M, one can specify a discrete magnetic flux valued in H2 (M,ZN). This flux is encoded in the AdS/CFT correspondence in terms of a five-dimensional topological field theory with Chern-Simons action. A similar topological field theory in seven dimensions governs the space of “conformal blocks ” of the six-dimensional (0, 2) conformal field theory. December
Anti de Sitter space and holography
, 1998
"... 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 ..."
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Cited by 372 (7 self)
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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 AdS5×S5 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. February
