On the holographic dual of a topological symmetry operator

Journal Article · 06 August 2024 · Physical Review. D.

DOI: https://doi.org/10.1103/PhysRevD.110.046007 · OSTI ID:2426995

Heckman, Jonathan J.; Hübner, Max; Murdia, Chitraang

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 $p$ -form symmetries for $p\ge 0$ 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, ( $-m$ )-form symmetries for $m\ge 2$ . Published by the American Physical Society 2024

• Research Organization: Univ. of Pennsylvania, Philadelphia, PA (United States)
• Sponsoring Organization: USDOE Office of Science (SC); USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: SC0013528
• OSTI ID: 2426995
• Journal Information: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 4 Vol. 110; ISSN PRVDAQ; ISSN 2470-0010
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English