In this talk I will show how the essential ingredients of recent calculations of the Page curve of an evaporating black hole can be used to generalize a recent argument against global symmetries beyond the AdS/CFT correspondence to more realistic theories of quantum gravity, illustrating a close connection between the absence of global symmetries and a unitary resolution of the black hole information problem. I'll also give several low-dimensional examples of quantum gravity theories which do not have a unitary resolution of the black hole information problem, and which therefore can and do have global symmetries. Motivated by this discussion, I'll conjecture that in a certain sense Euclidean quantum gravity is equivalent to holography. Based on recent work with Edgar Shaghoulian.
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