Abstract
We initiate a study of subregion dualities, entropy, and redundant encoding of bulk points in holographic theories deformed by Toverline{T} and its generalizations. This includes both cut off versions of Anti de Sitter spacetime, as well as the generalization to bulk de Sitter spacetime, for which we introduce two additional examples capturing different patches of the bulk and incorporating the second branch of the square root dressed energy formula. We provide new calculations of entanglement entropy (EE) for more general divisions of the system than the symmetric ones previously available. We find precise agreement between the gravity side and deformed-CFT side results to all orders in the deformation parameter at large central charge. An analysis of the fate of strong subadditivity for relatively boosted regions indicates nonlocality reminiscent of string theory. We introduce the structure of operator algebras in these systems. The causal and entanglement wedges generalize to appropriate deformed theories but exhibit qualitatively new behaviors, e.g. the causal wedge may exceed the entanglement wedge. This leads to subtleties which we express in terms of the Hamiltonian and modular Hamiltonian evolution. Finally, we exhibit redundant encoding of bulk points, including the cosmological case.
Highlights
In recent years, holographic dualities have developed in several important ways
We find that all contributions of the deformation to the entropy turn out to localize at the endpoints of the entangling region ρ0 L
L is the size of the interval for which we compute the entanglement entropy (EE), n is the replica index, and ρ is the radial distance to one of the endpoints
Summary
In. AdS/CFT, the association of bulk regions with appropriate operator algebras in the dual ‘boundary’ theory leads to an in-principle method for their approximate reconstruction [1,2,3,4,5], moving beyond the original HKLL prescription developed earlier in [6].1. It is an extraordinarily fruitful case study for quantum gravity, AdS/CFT is neither phenomenologically viable nor generic in string theory, with its special asymptotic boundary and bulk geometry being highly unrealistic In another line of development, the T Tdeformation [9,10,11,12] and its generalizations such as [13,14,15,16] enable us to isolate a finite patch of spacetime not intersecting the original boundary [17]. In the case of the entanglement wedge, we specify a division of the system which semiclassically corresponds to the division across the extremal surface of [34, 35] as in [1, 2]
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