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

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 $\sqrtρ$ 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.

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