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Conformal partial wave analysis of AdS amplitudes for dilaton-axion four-point functions
High Energy Physics - Theory · Submitted 18 Dec 2000
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The anomalous dimensions $\eta(l)$ are calculated at order $\mathcal{O}(N^{-2})$ for both $2^{-{1/2}}(-\tilde{\Phi}\tilde{\Phi} + \tilde{C}\tilde{C})$ and $2^{-{1/2}}(\tilde{\Phi}\tilde{C} + \tilde{C}\tilde{\Phi})$ and are found to be the same, proving $U(1)_Y$ symmetry.
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The abstract, sentence by sentence
Operator product expansions are applied to dilaton-axion four-point functions. In the expansions of the bilocal fields $\tilde{\Phi}\tilde{\Phi}$, $\tilde{C}\tilde{C}$ and $\tilde{\Phi}\tilde{C}$, the conformal fields which are symmetric traceless tensors of rank $l$ and have dimensions $\delta=2+l$ or $8+l+\eta(l)$ and $\eta(l)=\mathcal{O}(N^{-2})$ are identified. The unidentified fields have dimension $\delta=\lambda+l+\eta(l)$ with $\lambda\geq 10$. The anomalous dimensions $\eta(l)$ are calculated at order $\mathcal{O}(N^{-2})$ for both $2^{-{1/2}}(-\tilde{\Phi}\tilde{\Phi} + \tilde{C}\tilde{C})$ and $2^{-{1/2}}(\tilde{\Phi}\tilde{C} + \tilde{C}\tilde{\Phi})$ and are found to be the same, proving $U(1)_Y$ symmetry. The relevant coupling constants are given at order $\mathcal{O}(1)$.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Operator product expansions are applied to dilaton-axion four-point functions. | method 0.71 | 0.71 | 0.05 | asserted 0.99 |
| s1 | In the expansions of the bilocal fields $\tilde{\Phi}\tilde{\Phi}$, $\tilde{C}\tilde{C}$ and $\tilde{\Phi}\tilde{C}$, the conformal fields which are symmetric traceless tensors of rank $l$ and have dimensions $\delta=2+l$ or $8+l+\eta(l)$ and $\eta(l)=\mathcal{O}(N^{-2})$ are identified. | result 0.84 | 0.83 | 0.15 | asserted 1.00 |
| s2 | The unidentified fields have dimension $\delta=\lambda+l+\eta(l)$ with $\lambda\geq 10$. | result 0.80 | 0.55 | 0.07 | asserted 1.00 |
| s3 | The anomalous dimensions $\eta(l)$ are calculated at order $\mathcal{O}(N^{-2})$ for both $2^{-{1/2}}(-\tilde{\Phi}\tilde{\Phi} + \tilde{C}\tilde{C})$ and $2^{-{1/2}}(\tilde{\Phi}\tilde{C} + \tilde{C}\tilde{\Phi})$ and are found to be the same, proving $U(1)_Y$ symmetry. | result 0.96 | 0.92 | 0.45 | asserted 1.00 |
| s4 | The relevant coupling constants are given at order $\mathcal{O}(1)$. | result 0.98 | 0.82 | 0.08 | asserted 1.00 |
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Original abstract
Operator product expansions are applied to dilaton-axion four-point functions. In the expansions of the bilocal fields $\tilde{\Phi}\tilde{\Phi}$, $\tilde{C}\tilde{C}$ and $\tilde{\Phi}\tilde{C}$, the conformal fields which are symmetric traceless tensors of rank $l$ and have dimensions $\delta=2+l$ or $8+l+\eta(l)$ and $\eta(l)=\mathcal{O}(N^{-2})$ are identified. The unidentified fields have dimension $\delta=\lambda+l+\eta(l)$ with $\lambda\geq 10$. The anomalous dimensions $\eta(l)$ are calculated at order $\mathcal{O}(N^{-2})$ for both $2^{-{1/2}}(-\tilde{\Phi}\tilde{\Phi} + \tilde{C}\tilde{C})$ and $2^{-{1/2}}(\tilde{\Phi}\tilde{C} + \tilde{C}\tilde{\Phi})$ and are found to be the same, proving $U(1)_Y$ symmetry. The relevant coupling constants are given at order $\mathcal{O}(1)$.
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3 arXiv papers cite this in 3 sentences
Papers citing it
Uses its data or values 2 papers
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To order $a^3$, the anomalous dimensions read [equation] where the tree-level and one-loop contributions $γ^(1)$ and $γ^(2)$ have been derived in [ref] and [ref] , respectively, while the two-loop contribution $γ^(3)$ constitutes a new result.[ Note that the formula for $γ^(3)$ quoted above is strictly speaking only valid for spins $ℓ≥6$.
Two-loop supergravity on AdS$_5\times$S$^5$ from CFT · Introduction · 0.86
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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 $Δ_t,ℓ = 2t+ℓ+γ_t,ℓ$.
Bootstrapping mixed correlators in $\mathcal{N}=4$ Super Yang-Mills · Known analytic results · 0.88
Cites it as support 1 paper
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The few known results for $$ from top-down computations in supergravity suggest that this may be the case for all $n$ [ref] .
Holographic Reconstruction of AdS Exchanges from Crossing Symmetry · Introduction · 0.98
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