Closing the loop on Φ⁴ in AdS₃

We compute the one-loop correction to the CFT data of all double-trace operators [ϕϕ]_n,ℓ for a Φ⁴ theory in AdS₃, for arbitrary values of n, ℓ, and of the scaling dimension ∆_ϕ > 1. Working in the spectral representation, the t-channel one-loop bubble diagram is reduced to a product of spectral integrals dressed by the conformal 6j symbol. Both the spectral integrals and the subsequent sums over residues are performed analytically, yielding finite closed-form expressions for the anomalous dimensions in terms of higher hypergeometric functions. We discuss the structure of the results, including their large-spin and high-energy behaviors, and show that the anomalous dimensions are completely monotonic in spin.