AdS correction to the Faddeev-Kulish state: migrating from the flat peninsula

The IR finiteness of S-matrix in flat spacetime is tied to the Faddeev-Kulish dressed state, which suggests dressing the Fock space scattering state with the soft photon modes. We instigate a construction for the Faddeev-Kulish dressed state in the language of AdS/CFT. A salient feature of AdS spacetime is that it acquits itself as a quintessential IR regulator. The IR divergences will take shape after taking the zoomed in limit. We explore the Faddeev-Kulish dressed state to account for the AdS radius corrections. The Wilson line dressing stands as a guiding principle in the study of AdS radius-corrected Faddeev-Kulish dressing. We construct the modes of the Wilson line dressed massive scalar field implementing vanilla HKLL reconstruction since the field is simply free field. This simplification is owing to the use of soft photon modes in the Wilson line dressing. We map the AdS radius-corrected soft photon modes in terms of CFT current operators. We invert this mapping, use the mapping in the Wilson line dressing, and express the AdS radius-corrected Faddeev-Kulish dressed state.

Automated summary

The IR finiteness of the S-matrix in flat spacetime is related to the Faddeev-Kulish dressed state, which suggests dressing the Fock space scattering state with soft photon modes. We construct the Faddeev-Kulish dressed state in the AdS/CFT language. AdS spacetime serves as an effective IR regulator, and the IR divergences emerge after taking the zoomed-in limit. We use the Faddeev-Kulish dressed state to account for AdS radius corrections, focusing on the Wilson line dressing principle.