[論文レビュー] On the Holographic Dual of a Topological Symmetry Operator

Jonathan J. Heckman, Max Hübner+1 more|arXiv (Cornell University)|Jan 17, 2024

Black Holes and Theoretical Physics被引用数 6

ひとこと要約

本論文は、AdS/CFT において、境界のトポロジカル対称性演算子が純粋にトポロジカルなバルク双対を持たないと主張する。代わりに、それらのバルク対応物は応力-エネルギーを源し、非トポロジカルなブレイン様のオブジェクトとして現れ、p ≥ 0 のバルク全球 p-形式対称性が存在しないことを示唆する。

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 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 $m \geq 2$.

研究の動機と目的

• Motivate and analyze the holographic dual of boundary topological symmetry operators within AdS/CFT.
• Show that bulk duals must couple to the metric and are not purely topological.
• Argue the absence of global p-form symmetries in asymptotically AdS spacetimes and extend insights to non-invertible symmetries.
• Discuss the role of SymTFTs in capturing global symmetries and their bulk realization.

提案手法

• Consider a D-dimensional CFT with a topological symmetry operator N supported on a closed q-manifold Y, defining a p-form symmetry with p+q=D-1.
• Use bulk reconstruction and entanglement wedge arguments to infer the properties of the bulk dual ˜N.
• Argue via Euclidean and Lorentzian analyses that the bulk dual ˜N is not purely topological because it must source stress-energy.
• Relate the boundary SymTFT(D+1) framework to its bulk gravitational realization and the absence of bulk global symmetries.

実験結果

リサーチクエスチョン

• RQ1 Does a boundary topological symmetry operator have a purely topological bulk dual in AdS/CFT?
• RQ2 How does bulk reconstruction constrain the nature of the bulk dual of boundary symmetry operators?
• RQ3 Do global p-form symmetries exist in asymptotically AdS spacetimes, including non-invertible cases?
• RQ4 How does the SymTFT picture encode the bulk/boundary relationship of global symmetries in holography?
• RQ5 Can we extend the notion to (-m)-form symmetries for m ≥ 2 in general QFTs and their holographic duals?

主な発見

• The bulk dual of a boundary topological symmetry operator exists but cannot be purely topological; it must couple to bulk metric fluctuations and carry non-topological worldvolume dynamics.
• Entanglement wedge reconstruction implies that the bulk object sourcing the symmetry operator has finite bulk extent and contributes stress-energy, leading to non-topological behavior.
• There are no global p-form symmetries (p ≥ 0) in asymptotically AdS spacetimes within this framework, including non-invertible cases.
• The SymTFT framework captures the global symmetries of a QFT and naturally extends as a subsector of the holographic bulk, with the bulk becoming the dynamics that encodes symmetry information.
• For (-1)-form symmetries, the paper outlines a holographic interpretation as parameter-space walls or interpolating bulk geometries, maintaining non-topological features.