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

Abstract

Okuda and Penedones (OP) \cite{Okuda:2010ym} showed the existence of a double scaling limit of four point correlators in ${\cal N}=4$ Supersymmetric Yang Mills (SYM) theory in four spacetime dimensions (4$d$) dual to the flat space limit of tree-level string amplitude in $\mathbb{R}^{1,9}$ with external kinematics in $\mathbb{R}^{1,4}$. 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 (${\I}^{+}$). This is done by mapping the set of correlators in ${\cal N} = 4$ SYM theory (in the double scaling limit) to ${\I}^{+}$, which is the conformal boundary of all asymptotically flat spacetimes. A Carroll CFT thus emerges in the infinite 't Hooft coupling limit of ${\cal N} = 4$ SYM theory. 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 $\frac{1}{2}$ BPS sector of ${\cal N} = 4$ SYM theory 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.