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 R1, R2 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 R1, R2 to leading order in the bulk Newton constant G, and where the bulk duals are dominated by classical bulk geometries g1, g2. For states of fixed area on the R1, R2 HRT-surfaces, we argue that the bulk geometry g1#g2 dual to the newly sewn state is given by deleting the entanglement wedges of R1, R2 from g1, g2, gluing the remaining complementary entanglement wedges of R¯1,R¯2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\overline{R}}_1,{\overline{R}}_2 $$\end{document} 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 ρ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sqrt{\rho } $$\end{document} 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.