The authors derive new propagator identities that yield holographic representations for 5- and 6-point global scalar conformal blocks and obtain closed-form direct-channel decompositions of a class of higher-point AdS diagrams.
Loops in the Bulk
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abstract
We initiate a systematic investigation of Mellin amplitudes of Witten diagrams to all loop levels, by introducing integral recursion relations among them. Focusing on the scalar effective theories in AdS with the simplest type of interactions, the integral kernel that triggers the recursion obeys universal rules. As a first application, analytic properties of a 4-point triangle diagram is analyzed with this method.
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Computes closed-form one-loop anomalous dimensions for all double-trace operators [φφ]_{n,ℓ} in Φ⁴ theory in AdS₃ for arbitrary n, ℓ and Δ_φ > 1.
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Propagator identities, holographic conformal blocks, and higher-point AdS diagrams
The authors derive new propagator identities that yield holographic representations for 5- and 6-point global scalar conformal blocks and obtain closed-form direct-channel decompositions of a class of higher-point AdS diagrams.
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Closing the loop on $\Phi^4$ in AdS$_3$
Computes closed-form one-loop anomalous dimensions for all double-trace operators [φφ]_{n,ℓ} in Φ⁴ theory in AdS₃ for arbitrary n, ℓ and Δ_φ > 1.