AdS correction to the Faddeev-Kulish state: Migrating from the Flat Peninsula

TL;DR

This paper extends the Faddeev-Kulish state construction to AdS spacetime, using Wilson line dressings and AdS/CFT correspondence to incorporate AdS radius corrections and address IR divergences.

Contribution

It introduces a method to incorporate AdS radius corrections into Faddeev-Kulish states using Wilson line dressings within the AdS/CFT framework.

Findings

Constructed AdS radius-corrected Faddeev-Kulish states.

Mapped soft photon modes to CFT current operators.

Simplified field reconstruction using vanilla HKLL.

Abstract

The IR finiteness of $\mathcal{S}$-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 \textit{``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.