2026/07/29 by Avinandan Mondal
Physics and Astronomy · Mathematics · #hep-th #gr-qc #math-ph #math.MP
31+epsilon pages. 3 figures. Comments are welcome
arxiv created 2026/07/29 · arxiv updated 2026/07/31
Within the semi-classical regime of AdS/CFT correspondence, we consider the limit where the bulk dynamical field is linearized metric perturbations satisfying linearized Einstein equations over background pure AdS spacetime. AdS/CFT correspondence gives us a holographic map, which is an isometric embedding map of the GNS Hilbert space of linearized gravity in the bulk (w.r.t. the AdS-invariant vacuum) to the GNS Hilbert space of CFT in the boundary (w.r.t. the Minkowski-invariant vacuum). We assume that the map takes AdS-vacuum in the bulk to CFT-vacuum in the boundary and that it allows AdS-Rindler wedge reconstruction. Then using this map, we show that for a given ball-shaped region in the boundary A, the relative entropy of a bulk state w.r.t. the AdS vacuum in the algebra of causal wedge associated to A matches with the relative entropy of the dual CFT state w.r.t. the CFT vacuum in the algebra of CFT observables in A in the code subspace, which is known as Jafferis-Lewkowycz-Maldacena-Suh (JLMS) condition. Furthermore, for localized semi-classical coherent excitations in the causal wedge associated to A which corresponds to perturbed bulk geometry, we show rigorously using modular crossed product construction that the state-dependent part of entropy of the dual CFT state in the dressed Type-II algebra associated to A satisfies vacuum subtracted Hubeney-Rangamani-Takayanagi (HRT) formula.