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.
Highlights
Introduction and motivationIt is fair to say that the conformal Weyl symmetry which induces a local rescaling of a metric gμν (x) → Ω2(x)gμν (x) is still a fascinating local symmetry
It can be considered on the same footing as a gauge symmetry, a standpoint we shall adopt in the paper
Let us add in particular, its relationship with scale symmetry xμ → λxμ which confers the canonical dimension to a field
Summary
It is fair to say that the conformal Weyl symmetry which induces a local rescaling of a metric gμν (x) → Ω2(x)gμν (x) is still a fascinating local symmetry. The price to pay usually is to add in the theory a new Goldstone field which carries a non linear transformation law This legitimately raises the natural question whether the introduction of the above dilaton field σ as compensating field pertaining to the Weyl conformal symmetry, and the modification of the Einstein-Hilbert action into the action (1), stems from the usual generic construction of a Wess-Zumino term (or action or functional). This issue will be addressed in the present paper whose purpose is to provide a positive answer to this somewhat conceptual issue. Two appendices are devoted to the construction of the Wess-Zumino action according to Raymond Stora
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