AdS Asymptotic Symmetries from CFT Mirrors

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.