Holographic scattering and non-minimal RT surfaces

TL;DR

This paper explores how bulk scattering in AdS/CFT relates to entanglement structures, revealing that non-minimal RT surfaces impose additional constraints and suggest internal degrees of freedom are key to sub-AdS locality.

Contribution

It extends the connected wedge theorem by identifying new restrictions on non-minimal RT surfaces in AdS$_{2+1}$ geometries, linking bulk scattering to internal degrees of freedom.

Findings

Bulk scattering requires large entanglement and specific non-minimal surface restrictions.

Additional constraints on RT surfaces imply a complex entanglement structure involving internal degrees of freedom.

The identified restrictions are necessary but not sufficient for bulk scattering in mixed states.

Abstract

In the AdS/CFT correspondence, the causal structure of the bulk AdS spacetime is tied to entanglement in the dual CFT. This relationship is captured by the connected wedge theorem, which states that a bulk scattering process implies the existence of $O(1/G_N)$ entanglement between associated boundary subregions. In this paper, we study the connected wedge theorem in two asymptotically AdS$_{2+1}$ spacetimes: the conical defect and BTZ black hole geometries. In these settings, we find that bulk scattering processes require not just large entanglement, but also additional restrictions related to candidate RT surfaces which are non-minimal. We argue these extra relationships imply a certain CFT entanglement structure involving internal degrees of freedom. Because bulk scattering relies on sub-AdS scale physics, this supports the idea that sub-AdS scale locality emerges from internal degrees of freedom. While the new restriction that we identify on non-minimal surfaces is stronger than the initial statement of the connected wedge theorem, we find that it is necessary but still not sufficient to imply bulk scattering in mixed states.