  Asymptotic spacetime symmetries have been conjectured to play an important
role in quantum gravity. In this paper we study the breaking of asymptotic
symmetries associated with a null horizon boundary. In two-dimensions, these
symmetries are reparametrizations of the time parameter on the horizon. We show
how this horizon reparametrization symmetry is explicitly and spontaneously
broken in dilaton gravity and construct an effective action for these
pseudo-Goldstone modes using the on-shell gravitational action for a null
boundary. The variation of this action yields the horizon constraint equation.
This action is invariant under a 2 parameter subgroup of $SL(2)$
transformations, whose Noether charges we interpret via the membrane paradigm.
We place these results in the context of recent work on the near $AdS_2$/ near
$CFT_1$ correspondence. In this setting the horizon action characterizes the
infrared regime near the horizon and has a hydrodynamical sigma model form. We
also discuss our construction in General Relativity. In the three-dimensional
case there is a natural generalization of our results. However, in higher
dimensions, the variation of the effective action only yields the Raychaudhuri
equation for small perturbations of the horizon.
