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A note on Weyl gauge symmetry in gravity
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A scale invariant theory of gravity, containing at most two derivatives, requires, in addition to the Riemannian metric, a scalar field and (or) a gauge field. The gauge field is usualy used to construct the affine connection of Weyl geometry. In this note, we incorporate both the gauge field and the scalar field to build a generalised scale invariant Weyl affine connection. The Ricci tensor and the Ricci scalar made out of this generalised Weyl affine connection contain, naturally, kinetic terms for the scalar field and the gauge field. This provides a geometric interpretation for these terms. It is also shown that scale invariance in the presence of a cosmological constant and mass terms is not completely lost. It becomes a duality transformation relating various fields.
Forward citations
Cited by 2 Pith papers
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Conformal symmetry, SM and Gravity
A Weyl-invariant SM+mirror-dark-matter+gravity model is developed via algebraic renormalization; its conformal cohomology is claimed trivial, and the required counterterms could — the author concedes not conclusively ...
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A mirror right-handed copy of the standard model, sharing only gravity and SU(2), is claimed to be anomaly-free, proposed as dark matter, and wrapped in a Weyl-invariant early-universe solution.
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