Restricted Weyl Symmetry and Spontaneous Symmetry Breakdown of Conformal Symmetry

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 Poincaré symmetry.

arXiv comment14 pages

References in corpus (15)

• The galileon as a local modification of gravity
• Twenty Years of the Weyl Anomaly
• Quantum scale invariance, cosmological constant and hierarchy problem
• The Renormalization Group and Weyl-invariance
• Fake Conformal Symmetry in Conformal Cosmological Models
• Manifestly scale-invariant regularization and quantum effective operators
• Spontaneously Broken Conformal Symmetry: Dealing with the Trace Anomaly
• Two-loop scale-invariant scalar potential and quantum effective operators
• RG flow of Weyl-invariant dilaton gravity
• Running couplings with a vanishing scale anomaly
• Restricted Weyl invariance in four-dimensional curved spacetime
• Fake Conformal Symmetry in Unimodular Gravity
• Generating Einstein gravity, cosmological constant and Higgs mass from restricted Weyl invariance
• Critical gravity from four dimensional scale invariant gravity
• On Restricted Weyl Symmetry

Cited by in corpus (1)

• Quantum Theory of Weyl Invariant Scalar-tensor Gravity