Abstract
We develop a systematic approach to evaluating AdS loop amplitudes with spinning legs based on the spectral (or “split”) representation of bulk-to-bulk propagators, which re-expresses loop diagrams in terms of spectral integrals and higher-point tree diagrams. In this work we focus on 2pt one-loop Witten diagrams involving totally symmetric fields of arbitrary mass and integer spin. As an application of this framework, we study the contribution to the anomalous dimension of higher-spin currents generated by bubble diagrams in higher-spin gauge theories on AdS.
Highlights
The AdS/CFT correspondence provides a remarkable framework to handle quantum gravity on AdS space
Scattering amplitudes on AdS are identified with correlation functions in the dual CFT picture, through which the perturbative expansion of AdS amplitudes given by the loop expansion of Witten diagrams [1,2,3] is mapped to the 1/N expansion of CFT correlators
Motivated by the above considerations, in section 4.2.1 we study the contributions to the anomalous dimensions of higher-spin currents from 2pt bubble and e tadpole diagrams which appear in the difference of ∆ = 2 and ∆ = 1 scalar boundary conditions
Summary
The AdS/CFT correspondence provides a remarkable framework to handle quantum gravity on AdS space. This suggests that the non-trivial contributions to the anomalous dimension of higher-spin currents in the critical O(N ) model should arise from loop Witten diagrams appearing in the difference of ∆ = 2 and ∆ = 1 boundary conditions for the scalar While the latter prediction of the duality has been argued to follow from the duality with ∆ = 1 [69, 70], to date there has been no direct test of the duality for either boundary condition owing to the lack of a full quantum action in the bulk.. We point out a puzzle regarding the infinite summation over spin and the Witten diagram expansion
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