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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
DAMTP2008106 Fourpoint correlators with higher weight superconformal primaries in the AdS/CFT Correspondence
, 811
"... The fourpoint correlation function of two 1/2 BPS primaries of conformal weight ∆ = 2 and two 1/2BPS primaries of conformal weight ∆ = n is calculated in the large λ, large N limit. These operators are dual to Kaluza–Klein supergravity fields sk with masses m 2 = −4 and m 2 = n(n − 4). Given tha ..."
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Cited by 8 (1 self)
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The fourpoint correlation function of two 1/2 BPS primaries of conformal weight ∆ = 2 and two 1/2BPS primaries of conformal weight ∆ = n is calculated in the large λ, large N limit. These operators are dual to Kaluza–Klein supergravity fields sk with masses m 2 = −4 and m 2 = n(n − 4). Given that the existing formalism for evaluating sums of products of SO(6) tensors that determine the effective couplings is only suitable for primaries with small conformal dimensions, we make us of an alternative formalism based on harmonic polynomials introduced by Dolan and Osborn. We then show that the supergravity lagrangian relevant to the computation is of σmodel type (i.e., the fourderivative couplings vanish) and that the final result for the connected The AdS/CFT correspondence [1, 2, 3], the celebrated conjecture relating type IIB strings on AdS5×S 5 to N = 4 super YangMills theory, has received a lot of attention given the possibilities of extracting information from the strongly coupled gauge theory, by means of performing perturbative computations in the gravitational dual. However, this same property has made it difficult to find
Fourpoint functions of differentweight operators in the AdS/CFT correspondence
, 709
"... We calculate fourpoint correlation functions of two weight2 and two weight3 1 2BPS operators in N = 4 SYM in the large N limit in supergravity approximation. By the AdS/CFT conjecture, these operators are dual to AdS5 supergravity scalar fields s2 and s3 with mass m2 = −4 and m2 = −3 respectivel ..."
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Cited by 6 (0 self)
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We calculate fourpoint correlation functions of two weight2 and two weight3 1 2BPS operators in N = 4 SYM in the large N limit in supergravity approximation. By the AdS/CFT conjecture, these operators are dual to AdS5 supergravity scalar fields s2 and s3 with mass m2 = −4 and m2 = −3 respectively. This is the first nontrivial fourpoint function of mixedweight operators of lowest conformal dimensions. We show that the supergravityinduced fourpoint function splits into a “free” and a “quantum ” part, where the quantum contribution obeys nontrivial constraints coming from the insertion procedure in the gauge theory, in particular, it depends on only one function of the conformal crossratios.
The AdS/CFT Correspondence: Classical, Quantum, and . . .
, 2008
"... Certain aspects of the AdS/CFT correspondence are studied in detail. We investigate the oneloop mass shift to certain twoimpurity string states in lightcone string field theory on a plane wave background. We find that there exist logarithmic divergences in the sums over intermediate mode numbers ..."
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Cited by 1 (0 self)
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Certain aspects of the AdS/CFT correspondence are studied in detail. We investigate the oneloop mass shift to certain twoimpurity string states in lightcone string field theory on a plane wave background. We find that there exist logarithmic divergences in the sums over intermediate mode numbers which cancel between the cubic Hamiltonian and quartic “contact term”. Analyzing the impurity nonconserving channel we find that leading, nonperturbative terms predicted in the literature are in fact an artifact of these logarithmic divergences and vanish with them. We also argue that generically, every order in intermediate state impurities contributes to the mass shift at leading perturbative order. The same mass shift is also computed using an improved 3string vertex proposed by Dobashi and Yoneya. The result is compared with the prediction from nonplanar corrections in the BMN limit of N = 4 supersymmetric YangMills theory. It is found to agree at leading order – oneloop in YangMills theory – and is close but not quite in agreement at order two YangMills loops. Furthermore, in addition to the leading nonperturbative power in the ’t
Utrecht University
, 2007
"... The AdS/CFT correspondence, proposed by Maldacena, conjectures a duality between N = 4 SYM4 with a SU(N) gauge group and Type IIB string theory on AdS5×S5. In particular, in the large N limit, correlation functions in the strongly coupled gauge theory side can be calculated by considering the super ..."
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The AdS/CFT correspondence, proposed by Maldacena, conjectures a duality between N = 4 SYM4 with a SU(N) gauge group and Type IIB string theory on AdS5×S5. In particular, in the large N limit, correlation functions in the strongly coupled gauge theory side can be calculated by considering the supergravity approximation on the string theory side. In this thesis I will use this correspondence to compute a specific fourpoint correlator in the supergravity approximation. I will consider a fourpoint correlator of two weight2 and two weight3 12BPS operators. These operators correspond to supergravity scalar fields of mass m2 = −4 and m2 = −3 respectively. First it is shown that the effective Lagrangian reduces to a simple expression. This is then used to compute the onshell value, as prescribed by the AdS/CFT correspondence. To calculate this, a method to calculate vector and tensor exchange diagrams is extended to include couplings to currents which aren’t conserved onshell. Using this onshell action, the fourpoint function is calculated.
Imperial/TP/2011/LIU/01 Nextnexttoextremal Four Point Functions of N = 4 1/2BPS Operators in the AdS/CFT Correspondence
"... Four point functions of general N = 4 1/2BPS primary fields, satisfying the nextnexttoextremality condition ∆1 + ∆2 + ∆3 −∆4 = 4 are studied at large N and strong coupling. We apply new techniques to evaluate the effective couplings in supergravity, and confirm that the four derivative couplings ..."
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Four point functions of general N = 4 1/2BPS primary fields, satisfying the nextnexttoextremality condition ∆1 + ∆2 + ∆3 −∆4 = 4 are studied at large N and strong coupling. We apply new techniques to evaluate the effective couplings in supergravity, and confirm that the four derivative couplings arising in the fivedimensional supergravity vanish onshell. We then show that the four point amplitude resulting from supergravity naturally splits into a “free” and an interactive part which resembles an effective quartic interaction. The precise structure agrees with superconformal symmetry and supports the conjecture formulated by Dolan, Osborn and Nirschl regarding the strongly coupled form of four point correlators of chiral primary operators. We also evaluate the amplitude in large N free field SYM theory and discuss the results in the context of the correspondence. 1 ar
Contents
"... We use Integrability techniques to compute structure constants in N = 4 SYM to leading order. Three closed spin chains, which represent the single trace gaugeinvariant operators in N = 4 SYM, are cut into six open chains which are then sewed back together into some nice pants, the threepoint funct ..."
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We use Integrability techniques to compute structure constants in N = 4 SYM to leading order. Three closed spin chains, which represent the single trace gaugeinvariant operators in N = 4 SYM, are cut into six open chains which are then sewed back together into some nice pants, the threepoint function. The algebraic and coordinate Bethe ansatz tools necessary for this task are reviewed. Finally, we discuss the classical limit of our results, anticipating some predictions for quasiclassical string correlators in terms of algebraic curves. ar X iv