Entropy, extremality, euclidean variations, and the equations of motion

Dong, Xi; Lewkowycz, Aitor

doi:10.1007/jhep01(2018)081

Title: Entropy, extremality, euclidean variations, and the equations of motion

Journal Article · Wed Jan 17 00:00:00 EST 2018 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep01(2018)081· OSTI ID:1502460

^[1]; Lewkowycz, Aitor ^[2]

Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences; Univ. of California, Santa Barbara, CA (United States). Dept. of Physics
Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics

We study the Euclidean gravitational path integral computing the Rényi entropy and analyze its behavior under small variations. We argue that, in Einstein gravity, the extremality condition can be understood from the variational principle at the level of the action, without having to solve explicitly the equations of motion. This set-up is then generalized to arbitrary theories of gravity, where we show that the respective entanglement entropy functional needs to be extremized. We also extend this result to all orders in Newton’s constant G_N, providing a derivation of quantum extremality. Understanding quantum extremality for mixtures of states provides a generalization of the dual of the boundary modular Hamiltonian which is given by the bulk modular Hamiltonian plus the area operator, evaluated on the so-called modular extremal surface. This gives a bulk prescription for computing the relative entropies to all orders in G_N . We also comment on how these ideas can be used to derive an integrated version of the equations of motion, linearized around arbitrary states.

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Research Organization:: Institute for Advanced Study, Princeton, NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0009988

OSTI ID:: 1502460

Journal Information:: Journal of High Energy Physics (Online), Vol. 2018, Issue 1; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 90 works

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