AdS Witten diagrams to Carrollian correlators

Carrollian Conformal Field Theories (CFTs) have been proposed as co-dimension one holographic duals to asymptotically flat spacetimes as opposed to Celestial CFTs which are co-dimension two. In this paper, drawing inspiration from Celestial holography, we show by a suitable generalisation of the flat space limit of AdS that keeps track of the previously disregarded null direction, one can reproduce Carrollian CFT correlation functions from AdS Witten diagrams. In particular, considering Witten diagrams in AdS(4), we reproduce two and three-point correlation functions for three dimensional Carrollian CFTs in the so-called delta-function branch. Along the way, we construct non-trivial Carrollian three-point functions in the delta-branch by considering a collinear limit. We also obtain a generalised anti-podal matching condition that now depends on the retarded time direction.

Automated summary

In this paper, we generalize the flat space limit of AdS by considering the previously ignored null direction, thereby reproducing Carrollian CFT correlation functions from AdS Witten diagrams. Specifically, we reproduce two and three-point correlation functions for three dimensional Carrollian CFTs in the delta-function branch by considering Witten diagrams in AdS(4). Along the way, we construct non-trivial Carrollian three-point functions in the delta-branch by considering a collinear limit and obtain a generalized anti-podal matching condition dependent on the retarded time direction.