Asymptotic Symmetries, Holography and Topological Hair
Abstract
Asymptotic symmetries of AdS4 quantum gravity and gauge theory are derived by coupling the dual CFT3 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 AdS4 quantum gravity. An AdS4 analog of Minkowski "super-rotation" asymptotic symmetry is probed by 3D Einstein gravity, yielding CFT2 structure, via AdS3 foliation of AdS4 and the AdS3/CFT2 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 AdS4, 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 AdS4 than for Mink4, 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 AdS4, CFT3 and CFT2. The CFT2 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 AdS4 (holographic) "shadow" analog of Minkowski "memory" effects is derived. Lessons from AdS4 provide hints for better understanding Minkowski asymptotic symmetries, the 3D structure of its soft limits, and Minkowski holography.