Operator Product Expansion of the Lowest Weight CPOs in N=4 SYM_4 at Strong Coupling

A. C. Petkou; G. Arutyunov; S. Frolov

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Operator Product Expansion of the Lowest Weight CPOs in N=4 SYM_4 at Strong Coupling

G. Arutyunov, S. Frolov, A. C. Petkou

High Energy Physics - Theory · Submitted 19 May 2000

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The authors' main claim We present a detailed analysis of the 4-point functions of the lowest weight chiral primary operators $O^{I} \sim \tr \phi^{(i}\phi^{j)}$ in $\N =4$ SYM$_4$ at strong coupling and show that their structure is compatible with the predictions of AdS/CFT correspondence.

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CitationA. C. Petkou, G. Arutyunov, S. Frolov. "Operator Product Expansion of the Lowest Weight CPOs in N=4 SYM_4 at Strong Coupling." arXiv:hep-th/0005182 (2000). https://pith.science/paper/J2ZWRB3T

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We present a detailed analysis of the 4-point functions of the lowest weight chiral primary operators $O^{I} \sim \tr \phi^{(i}\phi^{j)}$ in $\N =4$ SYM$_4$ at strong coupling and show that their structure is compatible with the predictions of AdS/CFT correspondence. In particular, all power-singular terms in the 4-point functions exactly coincide with the contributions coming from the conformal blocks of the CPOs, the R-symmetry 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 3-point functions of scalar and vector double-trace operators with approximate dimensions 4 and 5 respectively. We also find that the conformal dimensions of certain towers of double-trace operators in the {\bf 105}, {\bf 84} and {\bf 175} irreps are non-renormalized. We show that, despite the absence of a non-renormalization theorem for the double-trace operator in the {\bf 20} irrep, its anomalous dimension vanishes. As by-products 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.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We present a detailed analysis of the 4-point functions of the lowest weight chiral primary operators $O^{I} \sim \tr \phi^{(i}\phi^{j)}$ in $\N =4$ SYM$_4$ at strong coupling and show that their structure is compatible with the predictions of AdS/CFT correspondence.	contribution 0.98	0.96	0.75	asserted 0.84
s1	In particular, all power-singular terms in the 4-point functions exactly coincide with the contributions coming from the conformal blocks of the CPOs, the R-symmetry current and the stress tensor.	result 1.00	0.84	0.22	asserted 1.00
s2	Operators dual to string modes decouple at strong coupling.	result 0.92	0.51	0.11	asserted 1.00
s3	We compute the anomalous dimensions and the leading $1/N^2$ corrections to the normalization constants of the 2- and 3-point functions of scalar and vector double-trace operators with approximate dimensions 4 and 5 respectively.	result 0.62	0.97	0.07	asserted 1.00
s4	We also find that the conformal dimensions of certain towers of double-trace operators in the {\bf 105}, {\bf 84} and {\bf 175} irreps are non-renormalized.	result 1.00	0.96	0.08	asserted 1.00
s5	We show that, despite the absence of a non-renormalization theorem for the double-trace operator in the {\bf 20} irrep, its anomalous dimension vanishes.	result 1.00	0.95	0.08	asserted 1.00
s6	As by-products 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.	result 0.85	0.96	0.04	asserted 1.00

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We present a detailed analysis of the 4-point functions of the lowest weight chiral primary operators $O^{I} \sim \tr \phi^{(i}\phi^{j)}$ in $\N =4$ SYM$_4$ at strong coupling and show that their structure is compatible with the predictions of AdS/CFT correspondence. In particular, all power-singular terms in the 4-point functions exactly coincide with the contributions coming from the conformal blocks of the CPOs, the R-symmetry 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 3-point functions of scalar and vector double-trace operators with approximate dimensions 4 and 5 respectively. We also find that the conformal dimensions of certain towers of double-trace operators in the {\bf 105}, {\bf 84} and {\bf 175} irreps are non-renormalized. We show that, despite the absence of a non-renormalization theorem for the double-trace operator in the {\bf 20} irrep, its anomalous dimension vanishes. As by-products 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.

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28 arXiv papers cite this in 40 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 24 sentences without a confident label

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Returning to the case $n=4$ we can, following [ref] , use the Barnes-Mellin expansion of the exponential e^-λ =1/2iπ ∫s Γ(-s) λ^s, with the integration contour running along the imaginary axes.

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Uses its data or values 3 papers

The anomalous dimensions at order $1/N^2$ of the long singlet operators with twist $2t$ and spin $ℓ$ in the OPE $2×2$ have been computed in [ref] .[For $t=2$ the results first appeared in [ref] .] For $t=2,3,…$ and $ℓ$ even one has ⟨γ_t,ℓ⟩=-4 (t-1) t (t+1) (t+2)/(ℓ+1) (ℓ+2 t+2)1/N^2 , [gammatl] where the conformal dimension is given by $Δ_t,ℓ = 2t+ℓ+γ_t,ℓ$.

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From [ref] , we know that $_[0,2,0],0$ is a double-trace operators constructed from $_2$ _[0,2,0], 0(x, y) =3/√(10 c (12c+1))y_M y_N δ_PQ _2^MP(x) _2^NQ(x) , _2^M_1 M_2(x) =tr(T^I_1T^I_2) (φ^(M_1_I_1(x)φ^M_2)_I_2(x) -1/6δ^M_1M_2 φ^P_I_1(x)φ_P, I_2(x)) [] where $M,N,P, Q$ are fundamental SO(6) index, $T^I$ are SU($N$) matrices and $φ^M_I$ is the fundamental scalar of $=4$ SYM.

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Its one-loop anomalous dimension is $Δ^(1)=3λ/4^2$ [ref] .

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Compares with it 1 paper

We obtain several OPE coefficients with two chiral primaries, which were known previously from the analysis of the $20'$ supergravity four-point function [ref] [equation] Note that our results have different normalizations as we use the tensor structures defined in Appendix [ref].

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Cites it as support 1 paper

The few known results for $$ from top-down computations in supergravity suggest that this may be the case for all $n$ [ref] .

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Cites it as background 8 papers

Also, in the case of 4-point functions there has been significant work in analysing the OPE limit of the Witten diagrams and its matching with the corresponding expected behaviour in the boundary CFT [ref] .

Implications of the AdS/CFT Correspondence on Spacetime and Worldsheet OPE Coefficients · Introduction · 0.90
We can say we know almost everything about the LLL; correlators from quite some time [ref] the HLL correlators are a bit exotic, they are mostly known from the gauge theory side [ref] ; the HHL starting from [ref] have recently been and continue to be an object of thorough research on both integrability/field theory and string theory sides; there have been some very promising attempts to construct also HHH correlators both from string [ref] and gauge theory sides [ref] .

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[ref] , and is contained in the $O_2^2 O_2^2$ OPE.

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