Scale Invariance vs. Conformal Invariance: Holographic Two-Point Functions in Horndeski Gravity

Understand

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.