De Sitter Observers and an Effective Field Theory of Horizon Edge Modes

We show that choosing a test observer in $d{S}_D$, specified by the framed embedding of their horizon $S^{D-2}$, spontaneously breaks the de Sitter and internal sphere isometries to diagonal rotations. We identify gravitational edge modes, described by low diffeomorphism jet fluctuations near the horizon sphere, as the associated Goldstone modes. We construct their membrane-like effective theory, organized in a small-gradient expansion. We find a class of nonlinear actions that at the quadratic order reproduce the edge-mode spectrum previously found in the one-loop gravitational $S^D$ path integral.