Modular Witten Diagrams and Quantum Extremality
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arXiv
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| Format: | Preprint |
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2025
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| author | Bhattacharya, Abhirup Parrikar, Onkar |
| author_facet | Bhattacharya, Abhirup Parrikar, Onkar |
| contents | We study entanglement entropy for ball-shaped regions in excited states of holographic conformal field theories. The excited states are prepared by the Euclidean path integral in the CFT with a source turned on for some double-trace operator, with a small, $O(1)$ amplitude $λ$. On the gravity side, the double-trace operator deforms the bulk geometry as well as the entanglement structure of the state of bulk matter fields. By the quantum extremal surface formula, this leads to a deformation of the shape of the entanglement wedge, an effect which becomes manifest in the entanglement entropy at $O(λ^2 G_N)$. On the CFT side, we explicitly calculate the entanglement entropy perturbatively in the source amplitude to $O(λ^2)$, in terms of modular-flowed correlation functions of double-trace operators. We then evaluate these modular-flowed correlation functions using Witten diagrams. This calculation involves a Schwinger-Keldysh contour ordering prescription in the bulk, which we motivate using analytic continuation from Euclidean replica correlators. Focusing on a particular graviton-exchange diagram, we rewrite it in a form where it manifestly reproduces the canonical energy term present in the quantum Ryu-Takayanagi formula, including the shape deformation of the entanglement wedge due to backreaction and quantum effects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11754 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modular Witten Diagrams and Quantum Extremality Bhattacharya, Abhirup Parrikar, Onkar High Energy Physics - Theory We study entanglement entropy for ball-shaped regions in excited states of holographic conformal field theories. The excited states are prepared by the Euclidean path integral in the CFT with a source turned on for some double-trace operator, with a small, $O(1)$ amplitude $λ$. On the gravity side, the double-trace operator deforms the bulk geometry as well as the entanglement structure of the state of bulk matter fields. By the quantum extremal surface formula, this leads to a deformation of the shape of the entanglement wedge, an effect which becomes manifest in the entanglement entropy at $O(λ^2 G_N)$. On the CFT side, we explicitly calculate the entanglement entropy perturbatively in the source amplitude to $O(λ^2)$, in terms of modular-flowed correlation functions of double-trace operators. We then evaluate these modular-flowed correlation functions using Witten diagrams. This calculation involves a Schwinger-Keldysh contour ordering prescription in the bulk, which we motivate using analytic continuation from Euclidean replica correlators. Focusing on a particular graviton-exchange diagram, we rewrite it in a form where it manifestly reproduces the canonical energy term present in the quantum Ryu-Takayanagi formula, including the shape deformation of the entanglement wedge due to backreaction and quantum effects. |
| title | Modular Witten Diagrams and Quantum Extremality |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2512.11754 |