  We consider Einstein-Horndeski gravity with a negative bare constant as a
holographic model to investigate whether a scale invariant quantum field theory
can exist without the full conformal invariance. Einstein-Horndeski gravity can
admit two different AdS vacua. One is conformal, and the holographic two-point
functions of the boundary energy-momentum tensor are the same as the ones
obtained in Einstein gravity. The other AdS vacuum, which arises at some
critical point of the coupling constants, preserves the scale invariance but
not the special conformal invariance due to the logarithmic radial dependence
of the Horndeski scalar. In addition to the transverse and traceless graviton
modes, the theory admits an additional trace/scalar mode in the scale invariant
vacuum. We obtain the two-point functions of the corresponding boundary
operators. We find that the trace/scalar mode gives rise to an non-vanishing
two-point function, which distinguishes the scale invariant theory from the
conformal theory. The two-point function vanishes in $d=2$, where the full
conformal symmetry is restored. Our results indicate the strongly coupled scale
invariant unitary quantum field theory may exist in $d\ge 3$ without the full
conformal symmetry. The operator that is dual to the bulk trace/scalar mode
however violates the dominant energy condition.
