The geodesics less traveled: Nonminimal RT surfaces and holographic scattering

A bstract The connected wedge theorem [1, 2] 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, [3] 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 [3] 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.