A note on Weyl invariance in gravity and the Wess–Zumino functional

Abstract

It is shown that the explicit calculation of the Wess–Zumino functional pertaining to the breaking term of the Weyl symmetry for the Einstein–Hilbert action allows to restore the Weyl symmetry by introducing the extra dilaton field as Goldstone field. Adding the Wess–Zumino counter-term to the Einstein–Hilbert action reproduces the usual Weyl invariant action used in standard literature. Further consideration might confer to the Einstein–Hilbert action a new status.