On the Holographic Dual of a Topological Symmetry Operator

We study the holographic dual of a topological symmetry operator in the context of the AdS/CFT correspondence. Symmetry operators arise from topological field theories localized on a subspace of the boundary CFT spacetime. We use bottom up considerations to construct the topological sector associated with their bulk counterparts. In particular, by exploiting the structure of entanglement wedge reconstruction we argue that the bulk counterpart has a non-topological worldvolume action, i.e., it describes a dynamical object. As a consequence, we find that there are no global $p$-form symmetries for $p\ge 0$ in asymptotically AdS spacetimes, which includes the case of non-invertible symmetries. Provided one has a suitable notion of subregion-subregion duality, our argument for the absence of bulk global symmetries applies to more general spacetimes. These considerations also motivate us to consider for general QFTs (holographic or not) the notion of lower-form symmetries, namely, $(-m)$-form symmetries for $m\ge 2$.