Ward identities under the frame transformations in curved spacetime

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.

arXiv comment14 pages, Accepted in Communications in Theoretical Physics

References in corpus (28)

• Heat kernel expansion: user's manual
• Inflation scenario via the Standard Model Higgs boson and LHC
• Standard Model Higgs boson mass from inflation
• Constraining f(R) Gravity as a Scalar Tensor Theory
• The conformal frame freedom in theories of gravitation
• On Inflation with Non-minimal Coupling
• Neutron-star mergers in scalar-tensor theories of gravity
• Question of quantum equivalence between Jordan frame and Einstein frame
• Einstein and Jordan frames reconciled: a frame-invariant approach to scalar-tensor cosmology
• Physical non-equivalence of the Jordan and Einstein frames
• Conformal-Frame (In)dependence of Cosmological Observations in Scalar-Tensor Theory
• Frame-dependence of higher-order inflationary observables in scalar-tensor theories
• Transformations between Jordan and Einstein frames: Bounces, antigravity, and crossing singularities
• On the maximum mass limit of neutron stars in scalar-tensor gravity
• Planck constraints on scalar-tensor cosmology and the variation of the gravitational constant
• Testing scalar-tensor theories and PPN parameters in Earth orbit
• Frame (In)equivalence in Quantum Field Theory and Cosmology
• Quantum Equivalence of $f(R)$ Gravity and Scalar-tensor Theories in the Jordan and Einstein Frames
• Ward Identity and Scattering Amplitudes for Nonlinear Sigma Models
• Scalar-tensor cosmology at the general relativity limit: Jordan vs Einstein frame
• Testing non-minimally coupled inflation with CMB data: a Bayesian analysis
• Anomalies, equivalence and renormalization of cosmological frames
• Non-minimal quartic inflation in classically conformal U(1)${}_X$ extended Standard Model
• Comparison of Frames: Jordan vs Einstein Frame for a Non-minimal Dark Energy Model
• Quartic inflation and radiative corrections with non-minimal coupling
• Dynamical equivalence of $f(R)$ gravity in Jordan and Einstein frames
• Topological anomalies from the path integral measure in superspace
• Consistency of equations of motion in conformal frames