2020
DOI: 10.1007/jhep12(2020)128
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Endpoint contributions to excited-state modular Hamiltonians

Abstract: We compute modular Hamiltonians for excited states obtained by perturbing the vacuum with a unitary operator. We use operator methods and work to first order in the strength of the perturbation. For the most part we divide space in half and focus on perturbations generated by integrating a local operator J over a null plane. Local operators with weight n ≥ 2 under vacuum modular flow produce an additional endpoint contribution to the modular Hamiltonian. Intuitively this is because operators with weight n ≥ 2 … Show more

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Cited by 5 publications
(14 citation statements)
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“…The endpoint contribution gives a correction to this result, arising from the fact that in general the unitary transformation doesn't factorize between A andĀ. Extending previous results [9] we find that the endpoint contribution involves operators we will refer to as light-ray moments of J (n) and its descendants. For planar surfaces the general result will be given in (6.8)-(6.10), and for perturbations with positive modular weight on a curved surface the general result will be given in (6.21).…”
Section: Jhep09(2021)074supporting
confidence: 76%
See 4 more Smart Citations
“…The endpoint contribution gives a correction to this result, arising from the fact that in general the unitary transformation doesn't factorize between A andĀ. Extending previous results [9] we find that the endpoint contribution involves operators we will refer to as light-ray moments of J (n) and its descendants. For planar surfaces the general result will be given in (6.8)-(6.10), and for perturbations with positive modular weight on a curved surface the general result will be given in (6.21).…”
Section: Jhep09(2021)074supporting
confidence: 76%
“…The result for δH A can be combined with an analogous result for the complementary region to obtain the first-order change in the extended or total modular Hamiltonian δ ↔ H = δH A − δHĀ. As in [9] we find that δ ↔ H is a sum of commutator and endpoint contributions.…”
Section: Jhep09(2021)074supporting
confidence: 63%
See 3 more Smart Citations