Doubly-scaled planar $\mathcal{N} = 4$ SYM & Carroll Holography

Abstract

In their seminal paper, Okuda and Penedones (OP) put forward an intriguing proposal towards holography in asymptotically flat spacetimes (AFS). They showed that the flat space limit of 4 point bosonic tree-level string amplitude in AdS$_{5}\, \times\, S^{5}$ is dual to a specific double scaling limit of 4 point correlator in four dimensional (4d) $\mathcal{N} = 4$ super Yang-Mills (SYM) theory. In this paper, we show that the resulting boundary correlators can be used to define a 4d Carrollian conformal field theory (CFT) on future null infinity. This is done by mapping the set of doubly scaled correlators in SYM to null infinity, the conformal boundary of AFS. A Carroll CFT thus emerges in the infinite 't Hooft coupling limit of $\mathcal{N} = 4$ SYM. We extend the OP analysis to higher point functions and show how the Gram conditions on flat space amplitude put constraints on the double scaling limit of SYM correlators. We then use the soft factorization theorem for dilatonic string amplitude to write a recursion relation for the $({1}/{2})$-BPS sector of $\mathcal{N} = 4$ SYM in the double scaling limit. Finally, we show that the essential ideas underlying such a double scaling limit can be used as a tool-kit to build a class of Carrollian correlators, and hence define a Carrollian CFT, via certain integral transforms of flat space amplitudes of non-gravitational effective field theories.