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arXiv · 2103.08636

Light-ray moments as endpoint contributions to modular Hamiltonians

Daniel Kabat·Gilad Lifschytz·Phuc Nguyen·Debajyoti Sarkar
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Abstract

We consider excited states in a CFT, obtained by applying a weak unitary perturbation to the vacuum. The perturbation is generated by the integral of a local operator $J^{(n)}$ of modular weight $n$ over a spacelike surface passing through $x = 0$. For $\vert n \vert \geq 2$ the modular Hamiltonian associated with a division of space at $x = 0$ picks up an endpoint contribution, sensitive to the details of the perturbation (including the shape of the spacelike surface) at $x = 0$. The endpoint contribution is a sum of light-ray moments of the perturbing operator $J^{(n)}$ and its descendants. For perturbations on null planes only moments of $J^{(n)}$ itself contribute.

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Daniel Kabat, Gilad Lifschytz, Phuc Nguyen, Debajyoti Sarkar. 2021-03-15. Light-ray moments as endpoint contributions to modular Hamiltonians. https://doi.org/10.1007/jhep09(2021)074

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