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

Donald Marolf

doi:10.1007/JHEP02(2020)152

paper

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

arXiv:1909.09330 · doi:10.1007/JHEP02(2020)152

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 $R ˉ_{1}, R ˉ_{2}$ 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 $ρ$ 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.

20 pages, 3 figures

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

Abstract

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