Results 1  10
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143
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
A nonrenormalization theorem for conformal anomalies” Nucl. Phys. B561
, 1999
"... We provide a nonrenormalization theorem for the coefficients of the conformal anomaly associated with operators with vanishing anomalous dimensions. Such operators include conserved currents and chiral operators in superconformal field theories. We illustrate the theorem by computing the conformal ..."
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Cited by 53 (13 self)
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We provide a nonrenormalization theorem for the coefficients of the conformal anomaly associated with operators with vanishing anomalous dimensions. Such operators include conserved currents and chiral operators in superconformal field theories. We illustrate the theorem by computing the conformal anomaly of 2point functions both by a computation in the conformal field theory and via the adS/CFT correspondence. Our results imply that 2 and 3point functions of chiral primary operators in N = 4 SU(N) SYM will not renormalize provided that a “generalized AdlerBardeen theorem ” holds. We further show that recent arguments connecting the nonrenormalizability of the above mentioned correlation functions to a bonus U(1)Y symmetry are incomplete due to possible U(1)Y violating contact terms. The tree level contribution to the contact terms may be set to zero by considering appropriately normalized operators. Nonrenormalizability of the above mentioned correlation functions, however, will follow only if these contact terms saturate by free fields. 1
Tinkertoys for Gaiotto Duality
 JHEP 1011 (2010) 099, arXiv:1008.5203 [hepth
"... We describe a procedure for classifyingN = 2 superconformal theories of the type introduced by Davide Gaiotto. Any curve, C, on which the 6D AN−1 SCFT is compactified, can be decomposed into 3punctured spheres, connected by cylinders. We classify the spheres, and the cylinders that connect them. Th ..."
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Cited by 45 (1 self)
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We describe a procedure for classifyingN = 2 superconformal theories of the type introduced by Davide Gaiotto. Any curve, C, on which the 6D AN−1 SCFT is compactified, can be decomposed into 3punctured spheres, connected by cylinders. We classify the spheres, and the cylinders that connect them. The classification is carried out explicitly, up through N = 5, and for several families of SCFTs for arbitrary N. These lead to a wealth of new Sdualities between Lagrangian and nonLagrangian N = 2 SCFTs. ar X iv
ChernSimons Theory with Vector Fermion Matter,” [arXiv:1110.4386 [hepth
"... We study three dimensional conformal field theories described by U(N) ChernSimons theory at level k coupled to massless fermions in the fundamental representation. By solving a SchwingerDyson equation in lightcone gauge, we compute the exact planar free energy of the theory at finite temperature ..."
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Cited by 39 (2 self)
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We study three dimensional conformal field theories described by U(N) ChernSimons theory at level k coupled to massless fermions in the fundamental representation. By solving a SchwingerDyson equation in lightcone gauge, we compute the exact planar free energy of the theory at finite temperature on R2 as a function of the ’t Hooft coupling λ = N/k. Employing a dimensional reduction regularization scheme, we find that the free energy vanishes at λ  = 1; the conformal theory does not exist for λ > 1. We analyze the operator spectrum via the anomalous conservation relation for higher spin currents, and in particular show that the higher spin currents do not develop anomalous dimensions at leading order in 1/N. We present an integral equation whose solution in principle determines all correlators of these currents at leading order in 1/N and present explicit perturbative results for all three point functions up to two loops. We also discuss a lightcone Hamiltonian formulation of this theory where a W ∞ algebra arises. The maximally supersymmetric version of our theory is ABJ model with one gauge group taken to be U(1), demonstrating that a pure higher spin gauge theory arises as a limit of string theory. ar X iv
The exact superconformal Rsymmetry minimizes τRR,” Nucl
 Phys. B
, 2005
"... We present a new, general constraint which, in principle, determines the superconformal U(1)R symmetry of 4d N = 1 SCFTs, and also 3d N = 2 SCFTs. Among all possibilities, the superconformal U(1)R is that which minimizes the coefficient, τRR, of its twopoint function. Equivalently, the superconform ..."
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Cited by 25 (3 self)
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We present a new, general constraint which, in principle, determines the superconformal U(1)R symmetry of 4d N = 1 SCFTs, and also 3d N = 2 SCFTs. Among all possibilities, the superconformal U(1)R is that which minimizes the coefficient, τRR, of its twopoint function. Equivalently, the superconformal U(1)R is the unique one with vanishing twopoint function with every nonR flavor symmetry. For 4d N = 1 SCFTs, τRR minimization gives an alternative to amaximization. τRR minimization also applies in 3d, where no condition for determining the superconformal U(1)R had been previously known. Unfortunately, this constraint seems impractical to implement for interacting field theories. But it can be readily implemented in the AdS geometry for SCFTs with AdS duals. June
OPEs and 3point correlators of protected operators
 in N = 4 SYM,” Nucl. Phys. B 626
, 2002
"... Two and threepoint correlation functions of arbitrary protected operators are constructed in N=4 SYM using analytic superspace methods. The OPEs of two chiral primary multiplets are given. It is shown that the npoint functions of protected operators for n ≤ 4 are invariant under U(1)Y and it is a ..."
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Cited by 21 (5 self)
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Two and threepoint correlation functions of arbitrary protected operators are constructed in N=4 SYM using analytic superspace methods. The OPEs of two chiral primary multiplets are given. It is shown that the npoint functions of protected operators for n ≤ 4 are invariant under U(1)Y and it is argued that this implies that the two and threepoint functions are not renormalised. It is shown explicitly how unprotected operators can be accommodated in the analytic superspace formalism in a way which is fully compatible with analyticity. Some new There has been a resurgence of interest in fourdimensional superconformal field theories over the past few years largely due to the impact of the Maldacena conjecture [1] and this has led to the discovery of many new and interesting results. Most of these results have concerned properties of short (series C) operators and their correlation functions derived both directly in
Correlation Functions of Large N ChernSimonsMatter Theories and Bosonization in Three Dimensions
, 2014
"... We consider the conformal field theory of N complex massless scalars in 2 + 1 dimensions, coupled to a U(N) ChernSimons theory at level k. This theory has a ’t Hooft large N limit, keeping fixed λ ≡ N/k. We compute some correlation functions in this theory exactly as a function of λ, in the large N ..."
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Cited by 21 (1 self)
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We consider the conformal field theory of N complex massless scalars in 2 + 1 dimensions, coupled to a U(N) ChernSimons theory at level k. This theory has a ’t Hooft large N limit, keeping fixed λ ≡ N/k. We compute some correlation functions in this theory exactly as a function of λ, in the large N (planar) limit. We show that the results match with the general predictions of Maldacena and Zhiboedov for the correlators of theories that have highspin symmetries in the large N limit. It has been suggested in the past that this theory is dual (in the large N limit) to the Legendre transform of the theory of fermions coupled to a ChernSimons gauge field, and our results allow us to find the precise mapping between the two theories. We find that in the large N limit the theory of N scalars coupled to a U(N)k ChernSimons theory is equivalent to the Legendre transform of the theory of k fermions coupled to a U(k)N ChernSimons theory, thus providing a bosonization of the latter theory. We conjecture that perhaps this duality is valid also for finite values of N and k, where on the fermionic side we should now have (for Nf flavors) a U(k)N−Nf/2 theory. Similar results hold for real scalars (fermions) coupled to the O(N)k ChernSimons theory.
Four Dimensional CFT Models with Rational Correlation Functions
, 2001
"... a)y, Ya.S. Stanev a)b)z, I.T. Todorov a) c)x ..."
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The CFT/AdS correspondence, massive gravitons and a connectivity index conjecture,” [ArXiv:hepth/0608089
"... We discuss the general question of which conformal field theories have dual descriptions in terms of quantum gravity theories on antide Sitter space. We analyze in detail the case of a deformed product of n conformal field theories (each of which has a gravity dual), and we claim that the dual desc ..."
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Cited by 15 (0 self)
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We discuss the general question of which conformal field theories have dual descriptions in terms of quantum gravity theories on antide Sitter space. We analyze in detail the case of a deformed product of n conformal field theories (each of which has a gravity dual), and we claim that the dual description of this is by a quantum gravity theory on a union of n antide Sitter spaces, connected at their boundary (by correlations between their boundary conditions). On this union of spaces, (n − 1) linear combinations of gravitons obtain a mass, and we compute this mass both from the field theory and from the gravity sides of the correspondence, finding the same result in both computations. This is the first example in which a graviton mass in the bulk of antide Sitter space arises continuously by varying parameters. The analysis of these deformed product theories leads us to suggest that field theories may be generally classified by a “connectivity index”, corresponding to the number of components (connected at the boundary) in the spacetime of the dual gravitational background. In the field theory this index roughly counts the number of independent gauge groups, but we do not have a precise general formula for the index. August