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

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 ofR 1 ,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 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. arXiv:1909.09330v1 [hep-th]

Including contributions from entanglement islands to the reflected entropy

“…There have also been holographic proposals for other measures of bipartite correlation such as entanglement negativity, odd entropy and entanglement wedge mutual information [25,[45][46][47][48][49]. Similarly, multipartite versions of the reflected entropy and entanglement of purification have also been proposed previously [50][51][52]. Although we have focused on the reflected entropy in this paper, the generalization essentially can be understood as applying the usual holographic formula after including the island in the entanglement wedge.…”

Modular zero modes and sewing the states of QFT

“…We argued that the local unitary that acts on |Ψ and creates the vacuum state ω is the cocycle u Ω|Ψ (t) in the large t limit. Ideas similar to sewing states of quantum field theory have appeared in various context, recently [21,22]. It would be interesting to explore the connection between our algebraic sewing prescription and sewing Euclidean path-integrals discussed in the literature.…”

Multipartite entanglement and topology in holography

“…Following [17] we do not view this as an issue for our construction. This gluing procedure was further formalized in [20] where it was applied to entanglement wedges glued across a common RT surface. In higher dimensions one must be careful that the choice of boundary regions gives a well defined connected entanglement wedge on which our procedure can be performed.…”