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CFT sewing as the dual of AdS cut-and-paste
oleh: Donald Marolf
| Format: | Article |
|---|---|
| Diterbitkan: | SpringerOpen 2020-02-01 |
Deskripsi
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 ¯ 1 , R ¯ 2 $$ {\overline{R}}_1,{\overline{R}}_2 $$ 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 ρ $$ \sqrt{\rho } $$ 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.