  The theory of scalar gravity proposed by Nordstr\"{o}m, and refined by
Einstein and Fokker, provides a striking analogy to general relativity. In its
modern form, scalar gravity appears as the low-energy effective field theory of
the spontaneous breaking of conformal symmetry within a CFT, and is AdS/CFT
dual to the original Randall-Sundrum I model, but without a UV brane. Scalar
gravity faithfully exhibits several qualitative features of the cosmological
constant problem of standard gravity coupled to quantum matter, and the
Weinberg no-go theorem can be extended to this case as well. Remarkably, a
solution to the scalar gravity cosmological constant problem has been proposed,
where the key is a very small violation of the scalar equivalence principle,
which can be elegantly formulated as a particular type of deformation of the
CFT. In the dual AdS picture this involves implementing Goldberger-Wise radion
stabilization where the Goldberger-Wise field is a pseudo-Nambu Goldstone
boson. In quantum gravity however, global symmetries protecting pNGBs are not
expected to be fundamental. We provide a natural six-dimensional gauge theory
origin for this global symmetry and show that the violation of the equivalence
principle and the size of the vacuum energy seen by scalar gravity can
naturally be exponentially small. Our solution may be of interest for study of
non-supersymmetric CFTs in the spontaneously broken phase.
