The Geodesics Less Traveled: Nonminimal RT Surfaces and Holographic Scattering

The connected wedge theorem states that in order to have a scattering process in the bulk, it is necessary to have $O(1/G_N)$ mutual information between certain "decision" regions in the boundary theory. While this large mutual information is not generally sufficient to imply scattering, arxiv:2404.15400 showed that for a certain class of geometries, bulk scattering is implied by a certain relation between two (possibly non-minimal) Ryu-Takayanagi surfaces. Here, we show that the 2-to-2 version of the theorem becomes an equivalence in pure AdS$_3$: large mutual information between appropriate boundary subregions is both necessary and sufficient for bulk scattering. This result allows us to extend the findings of arxiv:2404.15400 to a broader class of asymptotically AdS$_3$ spacetimes, which we illustrate with the spinning conical defect geometry. In contrast, we find that matter sources can disrupt this converse relation, and that the $n$-to-$n$ version of the theorem with $n>2$ lacks a converse even in the AdS$_3$ vacuum.