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Wet Hair: Global Symmetries in Entanglement Islands

A central conjecture in quantum gravity is the non-existence of global symmetries. As a fully unitary theory, there is no information loss in a UV complete quantum gravity theory. We see both these concepts reflected in the AdS/CFT correspondence, which tells us that dynamical processes in AdS are fully captured by a manifestly unitary CFT with no information loss. Furthermore, global symmetries of the CFT are dual to gauge symmetries in the AdS, which implies no global symmetry in the AdS. In this work, we provide concrete evidence for the connection between the non-existence of global symmetries and the absence of information loss in quantum gravity. We study the $\textit{island setups}$ in which a gravitational AdS is coupled with a nongravitational bath on its boundary. In such theories, the information in the AdS can be lost to the bath. We provide concrete examples with global symmetries in the island setup, from both the bottom-up and the top-down perspectives. We argue that these global symmetries are consistent due to $\textit{entanglement islands}$, in which holography is realized in a novel fashion. The global symmetries we construct are all mixed with spontaneously broken gauge symmetries. We will show that this fact has two implications: $\textbf{1)}$ The black hole hair is detectable in the bath (``wet hair"); $\textbf{2)}$ a resolution of a puzzle proposed by Harlow and Shaghoulian.