Abstract
Conformal tractors and twistors can be obtained via gauge reduction of the conformal Cartan geometry, thanks to the dressing field method. Perhaps surprisingly, it is possible to reduce the gauge symmetry further still. The Weyl symmetry can indeed be erased thanks to the tractor field, from which a dilaton is extracted. This suggests an alternative to the Weyl or conformal spontaneous symmetry breaking (SSB) that some authors proposed as improvement of the Standard Model or of inflationary cosmology, but also raises doubts as to the physical significance of such symmetries. Here, after gauge reduction via dressing, only the Lorentz gauge symmetry remains physically relevant, and the twistor field becomes — for all practical purposes — a Dirac spinor field. In a simple illustrative toy model, the latter acquires a mass through Lorentz SSB due to the VEV of the Weyl-invariant tractor field.
Highlights
JHEP06(2019)018 within this differential geometric setup, one can get ride of the Weyl gauge symmetry without spontaneous symmetry breaking (SSB), but rather in a non-dynamical way via the dressing field method (DFM), thereby questioning its physical meaning
The Weyl symmetry can be erased thanks to the tractor field, from which a dilaton is extracted. This suggests an alternative to the Weyl or conformal spontaneous symmetry breaking (SSB) that some authors proposed as improvement of the Standard Model or of inflationary cosmology, and raises doubts as to the physical significance of such symmetries
As a comment on existing literature, we highlight that our main results support the analysis of Jackiw and Pi [11] who assert that the Weyl symmetry in recently introduced cosmological models, notably [2], is ‘fake” and has no dynamical consequences
Summary
The dressing field method is a technically rather simple and conceptually powerful tool allowing to deal with gauge symmetries so as to reveal the physical degrees of freedom (d.o.f) of a theory in a way that differs markedly from both gauge fixing or spontaneous symmetry breaking mechanisms. One can consult [12] p.377 for a review with some interesting applications, and [13] for an assessment of its implications regarding philosophy of physics. This section is a nutshell presentation of the method and is the occasion of fixing some notation. We refer to [14] for the proofs of all the following assertions
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