OPEs and 3-point correlators of protected operators in N=4 SYM

Heslop, Paul; Howe, Paul

doi:10.1016/s0550-3213(02)00023-8

Cited by 75 publications

(101 citation statements)

References 70 publications

(88 reference statements)

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“…As shown in [25] for two points (x i , θ i ,θ i ) and (x j , θ j ,θ j ) we may define x iαα which is superconformally covariant and depends on (x i+ , θ i ) and (x j− ,θ j ). The superconformal invariants are theũ = x For N = 2 we consider the four point function 6) and show how the present discussion leads to the conditions of Eden et al [3,10]. In a similar fashion to (5.3) we may obtain using (2.11)…”

Section: Four Point Functionsmentioning

confidence: 55%

“…Primarily for N = 2, superconformal identities for correlation functions of various operators [2,3,4,5,6] have been obtained using harmonic superspace methods and such results have also been extended to the N = 4 case. It is particularly desirable to explore fully the implications for four point correlation functions since in this case the ordinary conformal group leaves these undetermined up to one or more arbitrary functions of two conformal invariants u, v.…”

Section: Introductionmentioning

confidence: 99%

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Superconformal symmetry, correlation functions and the operator product expansion

Dolan¹,

Osborn²

2002

Nuclear Physics B

238

444

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Superconformal transformations are derived for the N = 2, 4 supermultiplets corresponding to the simplest chiral primary operators. These are applied to two, three and four point correlation functions. When N = 4, results are obtained for the three point function of various descendant operators, including the energy momentum tensor and SU(4) current. For both N = 2 or 4 superconformal identities are derived for the functions of the two conformal invariants appearing in the four point function for the chiral primary operator. These are solved in terms of a single arbitrary function of the two conformal invariants and one or three single variable functions. The results are applied to the operator product expansion using the exact formula for the contribution of an operator in the operator product expansion in four dimensions to a scalar four point function. Explicit expressions representing exactly the contribution of both long and possible short supermultiplets to the chiral primary four point function are obtained. These are applied to give the leading perturbative and large N corrections to the scale dimensions of long supermultiplets.

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Section: Four Point Functionsmentioning

confidence: 55%

Section: Introductionmentioning

confidence: 99%

Superconformal symmetry, correlation functions and the operator product expansion

Dolan¹,

Osborn²

2002

Nuclear Physics B

238

444

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“…On the supergravity side, the corresponding fields arise from the Kaluza-Klein reduction along the 5-sphere of excitations of the metric and the self-dual 5-form field strength. The agreement between these correlators on both sides of the correspondence is possible because three-point functions of chiral primary operators are not renormalized [5][6][7][8][9][10].…”

Section: Jhep11(2014)076mentioning

confidence: 98%

Thresholds of large N factorization in CFT4: exploring bulk spacetime in AdS5

Garner

Ramgoolam

Wen

2014

J. High Energ. Phys.

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Large N factorization ensures that, for low-dimension gauge-invariant operators in the half-BPS sector of N = 4 SYM, products of holomorphic traces have vanishing correlators with single anti-holomorphic traces. This vanishing is necessary to consistently map trace operators in the CFT 4 to a Fock space of graviton oscillations in the dual AdS 5 . We investigate the regimes at which the CFT correlators do not vanish but become of order one in the large N limit, which we call a factorization threshold. Quite generally, we find the threshold to be when the product of the two holomorphic operator dimensions is of order N log N . Our analysis considers extremal and non-extremal correlators and correlators in states dual to LLM backgrounds, and we observe intriguing similarities between the the energy-dependent running coupling of non-abelian gauge theories and our threshold equations. Finally, we discuss some interpretations of the threshold within the bulk AdS spacetime.

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“…The problem has also been investigated using N = 4 on-shell superspace methods [96,97], via the study of nilpotent superconformal invariants, which had been introduced for OSp(1,N) in [98]. Similar non-renormalization effects may be derived for 1/4 BPS operators and their correlators as well [99]. Two and three point correlators have also been investigated for superconformal descendant fields; for the R-symmetry current in [91] and later in [101]; see also [100] and [102].…”

Section: Non-renormalization Of 2-and 3-point Functionsmentioning

confidence: 99%

Supersymmetric Gauge Theories and the Ads/CFT Correspondence

D’Hoker

Freedman

2004

Strings, Branes and Extra Dimensions

320

627

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In these lecture notes we first assemble the basic ingredients of supersymmetric gauge theories (particularly N=4 super-Yang-Mills theory), supergravity, and superstring theory. Brane solutions are surveyed. The geometry and symmetries of anti-de Sitter space are discussed. The AdS/CFT correspondence of Maldacena and its application to correlation functions in the the conformal phase of N=4 SYM are explained in considerable detail. A pedagogical treatment of holographic RG flows is given including a review of the conformal anomaly in four-dimensional quantum field theory and its calculation from five-dimensional gravity. Problem sets and exercises await the reader.

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OPEs and 3-point correlators of protected operators in N=4 SYM

Cited by 75 publications

References 70 publications

Superconformal symmetry, correlation functions and the operator product expansion

Superconformal symmetry, correlation functions and the operator product expansion

Thresholds of large N factorization in CFT4: exploring bulk spacetime in AdS5

Supersymmetric Gauge Theories and the Ads/CFT Correspondence

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