On the holographic dual of a topological symmetry operator
Jonathan J. Heckman, Max Hübner, Chitraang Murdia
Abstract
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 conformal field theory 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 nontopological world volume action, i.e., it describes a dynamical object. As a consequence, we find that there are no global <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>p</a:mi></a:math>-form symmetries for <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>p</c:mi><c:mo>≥</c:mo><c:mn>0</c:mn></c:math> in asymptotically anti–de Sitter spacetimes, which includes the case of noninvertible 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, (<e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mo>−</e:mo><e:mi>m</e:mi></e:math>)-form symmetries for <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>m</g:mi><g:mo>≥</g:mo><g:mn>2</g:mn></g:math>. Published by the American Physical Society 2024