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arXiv · 2104.04694

Restricted Weyl Symmetry and Spontaneous Symmetry Breakdown of Conformal Symmetry

Ichiro Oda
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Abstract

We elucidate the relation between the restricted Weyl symmetry and spontaneous symmetry breakdown of conformal symmetry. Using a scalar-tensor gravity, we show that the restricted Weyl symmetry leads to spontaneous symmetry breakdown of a global scale symmetry when the vacuum expectation value of a scalar field takes a non-zero value. It is then shown that this spontaneous symmetry breakdown induces spontaneous symmetry breakdown of special conformal symmetry in a flat Minkowski space-time, but the resultant Nambu-Goldstone boson is not an independent physical mode but expressed in terms of the derivative of the dilaton which is the Nambu-Goldstone boson of the global scale symmetry. In other words, the theories which are invariant under the general coordinate transformation and the restricted Weyl transformation exhibit a Nambu-Goldstone phase where both special conformal transformation and dilatation are spontaneously broken while preserving the Poincar\'{e} symmetry.

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Ichiro Oda. 2021-04-10. Restricted Weyl Symmetry and Spontaneous Symmetry Breakdown of Conformal Symmetry. https://doi.org/10.1142/s0217732321502035

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