Closing the loop on Φ4 in AdS3

A bstract We compute the one-loop correction to the CFT data of all double-trace operators [ ϕϕ ] n,ℓ for a Φ 4 theory in AdS 3 , 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 6 j 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.