Ward identities under the frame transformations in curved spacetime

TL;DR

This paper investigates the quantum inequivalence of scalar-tensor gravity theories in different frames, demonstrating that Ward identities and effective actions differ between the Jordan and Einstein frames under Weyl transformations.

Contribution

It reveals that quantum Ward identities are not preserved under frame transformations, highlighting a fundamental inequivalence at the quantum level in scalar-tensor theories.

Findings

Ward identities differ between frames

Effective actions are not equivalent

Quantum inequivalence of classical frames

Abstract

Scalar-tensor theories of gravity are considered to be competitors to Einstein's theory of general relativity for the description of classical gravity, as they are used to build feasible models for cosmic inflation. These theories can be formulated both in the Jordan and Einstein frame, which are related by a Weyl transformation with a field transformation, known together as a frame transformation. These theories formulated in the above two frames are often considered to be equivalent from the point of view of classical theory. However, this is no longer true from the quantum field theoretical perspective. In the present article, we show that the Ward identities derived in the above two frames are not connected through the frame transformation. This shows that the quantum field theories formulated in these two frames are not equivalent to each other. Moreover, this inequivalence is also shown by comparing the effective actions derived in these two frames.