This paper studies how familiar flat-space physics appears from a curved spacetime known from holography: anti–de Sitter space times a five-sphere (AdS5×S5). The authors focus on what happens when the AdS radius is sent to infinity (the “flat-space limit”) while the internal S5 also decompactifies (its radius grows). To keep control of the infinite set of modes tied to the sphere, they organize correlators into “master” propagators and master correlators that resum the whole tower of Kaluza–Klein modes. In plain terms, they package an infinite number of fields coming from the compact sphere into single objects and then study the flat limit of those objects.

They implement the flat-space limit in three related ways. First, they take the limit of master correlators defined at the AdS boundary. Those produce expressions that look like scattering amplitudes, but with external kinematics restricted to five dimensions and with extra complex auxiliary null vectors that encode the former sphere directions. Second, they keep the external points in the AdS×S bulk while taking the flat limit and only move to the boundary afterwards. This route, the authors argue, recovers flat-space amplitudes with unrestricted ten-dimensional kinematics. Third, they show the two limits (flat-space and the usual boundary limit) do not commute in general, but commutativity can be restored by analytically continuing the sphere so the bulk becomes AdS5×dS5. That continuation leads to formulae that suggest an interpretation in flat space with two time directions and with ten-dimensional kinematics subject to two null constraints.

Why this matters: many concrete holographic constructions, like type IIB string theory on AdS5×S5 dual to four-dimensional super Yang–Mills theory, include compact internal dimensions. When one takes a flat-space limit one expects to recover ten-dimensional physics, but the limit is subtle and can look singular. By working with master correlators that resum all half-BPS scalar correlators, the paper makes the role of the decompactifying sphere transparent. The approach also ties into recent work that identifies the flat-space limit in the bulk with a Carrollian limit on the boundary field theory (a formal limit where the speed of light goes to zero), thus providing a position-space bridge between AdS/CFT and flat-space holography.