In a recent paper, Raju showed that the essential features of the monogamy paradox for old flat space black holes could be modeled using a setup in empty anti–de Sitter, leading to a violation in the monogamy of entanglement there. A physically interesting question is whether such a violation in the monogamy of entanglement can be posed in empty flat space. The answer is not immediately clear since flat space gravity has an entirely different vacuum and infrared structure than the gapped and unique AdS vacuum, which was exploited in Raju’s toy model. We answer this question in the affirmative, with an explicit construction. We formulate the paradox in terms of monogamy of Clauser-Horne-Shimony-Holt correlations, which we use to quantify the monogamy of entanglement. Extending Raju’s analysis to empty flat space, within effective field theory, we show that the entanglement of approximately local bulk modes just outside a light cone with modes just inside the light cone as well as with modes situated far away at the past of future null infinity $({\mathcal{I}}_{-}^{+})$ gives rise to an O(1) violation in the monogamy of entanglement. This cannot be resolved by small corrections of O($\sqrt{G_N}$). The issues arising from the above-mentioned vacuum and infrared features unique to flat spacetime are dealt with by introducing a physically motivated boundary projector onto states below a given infrared cutoff, which allows us to construct suitable operators at $({\mathcal{I}}_{-}^{+})$ that give rise to the violation. We argue that the resolution of the paradox is that our spatially separated observables probe the same underlying degrees of freedom, i.e., such observables act on a nonfactorized Hilbert space arising from the Gauss constraint, thereby circumventing the conflict with monogamy of entanglement.

• Received 23 May 2022
• Accepted 4 August 2022

DOI:https://doi.org/10.1103/PhysRevD.106.086002

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society