AdS Asymptotic Symmetries from CFT Mirrors

Abstract

We study Kac-Moody asymptotic symmetries and memory effects in ${\text{AdS}}_4^{\text{Poincare}}$ gauge theory and (when accompanied by 4D gravity) in its holographic CFT${}_3$ dual. While such infinite-dimensional symmetries are absent in standard asymptotic analyses of ${\text{AdS}}_4$, we show how they arise with alternate AdS boundary conditions. In the 3D holographic description, these alternate boundary conditions correspond to a modified ${\widetilde{\text{CFT}}}_3$ obtained by Chern-Simons gauging of the CFT${}_3$ dual defined by standard boundary conditions, so that Kac-Moody symmetries then follow from the familiar Chern-Simons/Wess-Zumino-Witten correspondence. Apart from their own intrinsic interest, in abelian ${\text{AdS}}_4$ gauge theories these alternate boundary conditions are equivalent to standard boundary conditions imposed on electric-magnetic dual variables. In the holographic description this corresponds to 3D "mirror" symmetries connecting the original and modified CFTs. Further, in both abelian and non-abelian theories we show that the alternative/${\widetilde{\text{CFT}}}_3$ theory emerges at leading order in large Chern-Simons level from the correlators of the standard theory, upon incorporating large-wavelength limits in the holographically emergent dimension. We point out similarities and differences between 4D AdS and Minkowski gauge theories in their asymptotic symmetries, "soft" limits and memory effects.

arXiv commentVersion 2: Added clarifying comments/discussions, matches the published version

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• The Holographic Nature of Null Infinity
• Memory Effect in Anti-de Sitter Spacetime
• Source and Response Soft Charges for Maxwell Theory on $Ad{S}_d$