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 $p geq 0$ 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 $m geq 2$.
According to the article, the holographic dual of a topological symmetry operator in the AdS/CFT correspondence can be studied. These symmetry operators come from topological field theories localized on a subspace of the boundary CFT spacetime. The article uses bottom-up considerations to construct the topological sector associated with their bulk counterparts.
By analyzing the structure of entanglement wedge reconstruction, the article argues that the bulk counterpart of the topological symmetry operator has a non-topological worldvolume action. This means that it describes a dynamic object rather than a purely topological one.
As a result of this analysis, the article concludes that there are no global p-form symmetries for p greater than or equal to 0 in asymptotically AdS spacetimes, even for non-invertible symmetries. This conclusion holds true for a wider range of spacetimes if a suitable notion of subregion-subregion duality is considered.
Based on these conclusions, the article suggests considering the notion of lower-form symmetries, specifically (-m)-form symmetries for m greater than or equal to 2, for general quantum field theories, whether holographic or not.
Future Roadmap
Potential Challenges:
- Developing a suitable notion of subregion-subregion duality for more general spacetimes
- Investigating the implications of the absence of global p-form symmetries in asymptotically AdS spacetimes
- Understanding the behavior and properties of dynamical objects associated with topological symmetry operators
- Exploring the implications and applications of lower-form symmetries in general quantum field theories
Potential Opportunities:
- Advancing our understanding of the AdS/CFT correspondence and its implications for symmetry operators
- Expanding the knowledge of entanglement wedge reconstruction and its connection to the bulk dynamics
- Exploring new avenues in quantum field theories by considering lower-form symmetries
- Applying the findings to various areas of physics, such as condensed matter systems, high-energy physics, and quantum gravity
Conclusion:
The article emphasizes the study of the holographic dual of a topological symmetry operator in relation to the AdS/CFT correspondence. It argues that the bulk counterpart of this operator has a non-topological worldvolume action and, as a result, there are no global p-form symmetries for p greater than or equal to 0 in asymptotically AdS spacetimes. The conclusions apply to a wider range of spacetimes if subregion-subregion duality is considered. The article suggests exploring lower-form symmetries for general quantum field theories as a potential future direction.