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" ... I wanted to point out that there is one technical problem in your description... our theorem does not apply to any of the symmetries you mention here! And indeed in AdS/CFT they all can be unbroken. The reason is that they are all actually gauge symmetries, not global symmetries. For electric charge I guess you are familiar with that, but in gravitational theory such as general relativity then translations, Lorentz transformations, CPT, etc are also gauge symmetries: they are just diffeomorphisms. ... "