CFT sewing as the dual of AdS cut-and-paste

TL;DR

This paper explores how the CPT map in quantum field theory corresponds to a geometric cut-and-paste operation in the bulk AdS space, providing a new way to understand holographic duals of sewn states and multipartite reflected entropy.

Contribution

It introduces a bulk geometric interpretation of the CPT sewing operation in holography, extending the understanding of dual states and entanglement structures in AdS/CFT.

Findings

Bulk geometry after sewing is obtained by cutting and gluing entanglement wedges.

The construction generalizes to states with variable HRT surface areas.

Application to multipartite reflected entropy geometries.

Abstract

The CPT map allows two states of a quantum field theory to be sewn together over CPT-conjugate partial Cauchy surfaces $R_1,R_2$ to make a state on a new spacetime. We study the holographic dual of this operation in the case where the original states are CPT-conjugate within $R_1,R_2$ to leading order in the bulk Newton constant $G$, and where the bulk duals are dominated by classical bulk geometries $g_1,g_2$. For states of fixed area on the $R_1,R_2$ HRT-surfaces, we argue that the bulk geometry $g_1 \# g_2$ dual to the newly sewn state is given by deleting the entanglement wedges of $R_1,R_2$ from $g_1,g_2$, gluing the remaining complementary entanglement wedges of ${\bar R}_1, {\bar R}_2$ together across the HRT surface, and solving the equations of motion to the past and future. The argument uses the bulk path integral and assumes it to be dominated by a certain natural saddle. For states where the HRT area is not fixed, the same bulk cut-and-paste is dual to a modified sewing that produces a generalization of the canonical purification state $\sqrt{\rho}$ discussed recently by Dutta and Faulkner. Either form of the construction can be used to build CFT states dual to bulk geometries associated with multipartite reflected entropy.