000012188 001__ 12188
000012188 005__ 20250218124806.0
000012188 02470 $$ahttps://doi.org/10.1103/PhysRevD.102.045009$$2doi
000012188 037__ $$aTEXTUAL
000012188 037__ $$bArticle
000012188 041__ $$aeng
000012188 245__ $$a$T\overline{T}$, the entanglement wedge cross section, and the breakdown of the split property
000012188 269__ $$a2020-08-07
000012188 336__ $$aArticle
000012188 520__ $$aWe consider fine-grained probes of the entanglement structure of two-dimensional conformal field theories deformed by the irrelevant double-trace operator $T\overline{T}$ and its closely related but nonetheless distinct single-trace counterpart. For holographic conformal field theories, these deformations can be interpreted as modifications of bulk physics in the ultraviolet region of anti-de Sitter space. Consequently, we can use the Ryu-Takayanagi formula and its generalizations to mixed state entanglement measures to test highly nontrivial consistency conditions. In general, the agreement between bulk and boundary quantities requires the equivalence of partition functions on manifolds of arbitrary genus. For the single-trace deformation, which is dual to an asymptotically linear dilaton geometry, we find that the mutual information and reflected entropy diverge for disjoint intervals when the separation distance approaches a minimum, finite value that depends solely on the deformation parameter. This implies that the mutual information fails to serve as a geometric regulator which is related to the breakdown of the split property at the inverse Hagedorn temperature. In contrast, for the double-trace deformation, which is dual to anti-de Sitter space with a finite radial cutoff, we find all divergences to disappear including the standard quantum field theory ultraviolet divergence that is generically seen as disjoint intervals become adjacent. We furthermore compute reflected entropy in conformal perturbation theory. While we find formally similar behavior between bulk and boundary computations, we find quantitatively distinct results. We comment on the interpretation of these disagreements and the physics that must be altered to restore consistency. We also briefly discuss the $T\overline{J}$ and $J\overline{T}$ deformations. 
000012188 536__ $$oU.S. Department of Energy$$cDE-SC0009924
000012188 536__ $$oSimons Foundation
000012188 540__ $$a<p>Published by the American Physical Society under the terms of the <a href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International</a> license.</p>
000012188 542__ $$fCC BY
000012188 690__ $$aPhysical Sciences Division
000012188 691__ $$aEnrico Fermi Institute
000012188 691__ $$aKadanoff Center for Theoretical Physics
000012188 7001_ $$1https://orcid.org/0000-0002-3368-1215$$2ORCID$$aAsrat, Meseret$$uUniversity of Chicago
000012188 7001_ $$1https://orcid.org/0000-0003-4352-910X$$2ORCID$$aKudler-Flam, Jonah$$uUniversity of Chicago
000012188 773__ $$tPhysical Review D
000012188 8564_ $$9214e8787-cb50-41bd-8254-de9584e88353$$ePublic$$s815430$$uhttps://knowledge.uchicago.edu/record/12188/files/PhysRevD.102.045009.pdf
000012188 908__ $$aI agree
000012188 909CO $$ooai:uchicago.tind.io:12188$$pGLOBAL_SET
000012188 983__ $$aArticle