  We consider a nearly-AdS$_2$ gravity theory on the two-sided wormhole
geometry. We construct three gauge-invariant operators in NAdS which move bulk
matter relative to the dynamical boundaries. In a two-sided system, these
operators satisfy an SL(2) algebra (up to non-perturbative corrections). In a
semiclassical limit, these generators act like SL(2) transformations of the
boundary time, or conformal symmetries of the two sided boundary theory. These
can be used to define an operator-state mapping. A particular large N and low
temperature limit of the SYK model has precisely the same structure, and this
construction of the exact generators also applies. We also discuss approximate,
but simpler, constructions of the generators in the SYK model. These are
closely related to the "size" operator and are connected to the maximal chaos
behavior captured by out of time order correlators.
