Gravitational Contact Interactions -- Does the Jordan Frame Exist?

TL;DR

This paper investigates the existence of the Jordan frame in scalar-tensor theories by analyzing how graviton exchange induces contact interactions and affects the effective potential in different conformal frames.

Contribution

It demonstrates the discrepancy in the effective potential between the Einstein and Jordan frames due to contact interactions from graviton exchange in scalar-tensor theories.

Findings

Contact interactions always revert the theory to the Einstein frame.

Effective potential differs between frames, showing a frame discrepancy.

Contact terms are absorbed into couplings, affecting the renormalization group.

Abstract

Scalar--tensor theories, with Einstein Hilbert and non-minimal interactions, $\sim M^2R/2 -\alpha\phi^2R/12 $, have graviton exchange induced contact interactions. These always pull the theory back into a formal Einstein frame in which $\alpha$ does not exist. In the Einstein frame, contact terms are induced, that are then absorbed back into other couplings to define the effective potential (or equivalently, the renormalization group). We show how these effects manifest themselves in a simple model by computing the effective potential in both frames displaying the discrepancy.