Conformal renormalization of scalar-tensor theories

Understand

We study a conformally coupled scalar-tensor theory with a quartic potential possessing local conformal symmetry up to a boundary term.

• We show that requiring the restoration of the full local conformal symmetry fixes the counterterms that render the on-shell action finite.
• The building block of the resulting action is a conformally covariant tensor which is constructed out of the metric and the scalar field and it has the same conformal weight as the Weyl tensor.
• This allows us to obtain the counterterms for the scalar-tensor sector in a closed form.