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Polyakov-Mellin Bootstrap for AdS loops
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abstract
We consider holographic CFTs and study their large $N$ expansion. We use Polyakov-Mellin bootstrap to extract the CFT data of all operators, including scalars, till $O(1/N^4)$. We add a contact term in Mellin space, which corresponds to an effective $\phi^4$ theory in AdS and leads to anomalous dimensions for scalars at $O(1/N^2)$. Using this we fix $O(1/N^4)$ anomalous dimensions for double trace operators finding perfect agreement with \cite{loopal} (for $\Delta_{\phi}=2$). Our approach generalizes this to any dimensions and any value of conformal dimensions of external scalar field. In the second part of the paper, we compute the loop amplitude in AdS which corresponds to non-planar correlators of in CFT. More precisely, using CFT data at $O(1/N^4)$ we fix the AdS bubble diagram and the triangle diagram for the general case.
Forward citations
Cited by 3 Pith papers
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Bulk-to-bulk photon propagator in AdS
The bulk-to-bulk photon propagator in Euclidean AdS is derived in axial, Coulomb and covariant gauges, with the simplest position-space form in the Fried–Yennie gauge ξ=d/(d−2).
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Analytic Bootstrap for Logarithmic CFT
The leading large-spin anomalous dimension of double-trace operators in four-dimensional logarithmic CFTs behaves as γ0/ℓ^{τ_m}, where τ_m is the minimal twist, provided no operator has negative scaling dimension.
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From bulk loops to boundary large-N expansion
The singular part of a one-loop four-point Witten diagram with a double-particle cut equals a product of tree-level subdiagram coefficients divided by a mean-field-theory coefficient.
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