Asymptotic Symmetries, Holography and Topological Hair

Abstract

Asymptotic symmetries of AdS${}_4$ quantum gravity and gauge theory are derived by coupling the dual CFT${}_3$ to Chern-Simons gauge theory and 3D gravity in a "probe" large-level limit. The infinite-dimensional symmetries are shown to arise when one is restricted to boundary subspaces with effectively two-dimensional geometry. A canonical example of such a restriction occurs within the 4D subregion described by a Wheeler-DeWitt wavefunctional of AdS${}_4$ quantum gravity. An AdS${}_4$ analog of Minkowski "super-rotation" asymptotic symmetry is probed by 3D Einstein gravity, yielding CFT${}_2$ structure, via AdS${}_3$ foliation of AdS${}_4$ and the AdS${}_3$/CFT${}_2$ correspondence. The maximal asymptotic symmetry is however probed by 3D conformal gravity. Both 3D gravities have Chern-Simons formulation, manifesting their topological character. Chern-Simons structure is also shown to be emergent in the Poincare patch of AdS${}_4$, as soft/boundary limits of 4D gauge theory, rather than "put in by hand", with a finite effective Chern-Simons level. Several of the considerations of asymptotic symmetry structure are found to be simpler for AdS${}_4$ than for Mink${}_4$, such as non-zero 4D particle masses, 4D non-perturbative "hard" effects, and consistency with unitarity. The last of these, in particular, is greatly simplified, because in some set-ups the time dimension is explicitly shared by each level of description: Lorentzian AdS${}_4$, CFT${}_3$ and CFT${}_2$. The CFT${}_2$ structure clarifies the sense in which the infinite asymptotic charges constitute a useful form of "hair" for black holes and other complex 4D states. An AdS${}_4$ (holographic) "shadow" analog of Minkowski "memory" effects is derived. Lessons from AdS${}_4$ provide hints for better understanding Minkowski asymptotic symmetries, the 3D structure of its soft limits, and Minkowski holography.

typos corrected, references added, discussions of boundary conditions corrected and clarified

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Cited by in corpus (8)

• Black Hole Entropy and Soft Hair
• Holographic BCFTs and Communicating Black Holes
• The Holographic Nature of Null Infinity
• On the need for soft dressing
• Invariance of Unruh and Hawking radiation under matter-induced supertranslations
• Supertranslation Hair of Schwarzschild Black Hole: A Wilson Line Perspective
• Source and Response Soft Charges for Maxwell Theory on $Ad{S}_d$
• AdS Asymptotic Symmetries from CFT Mirrors