## Abstract

In two measures theories (TMT), in addition to the Riemannian measure of integration, being the square root of the determinant of the metric, we introduce a metric-independent density Φ in four dimensions defined in terms of scalars φ_{a} by Φ = ε^{μ} ^{ν} ^{ρ} ^{σ}ε_{a} _{b} _{c} _{d}(∂_{μ}φ_{a}) (∂_{ν}φ_{b}) (∂_{ρ}φ_{c}) (∂_{σ}φ_{d}). With the help of a dilaton field ϕ we construct theories that are globally scale invariant. In particular, by introducing couplings of the dilaton ϕ to the Gauss–Bonnet (GB) topological density -gϕ(Rμνρσ2-4Rμν2+R2) we obtain a theory that is scale invariant up to a total divergence. Integration of the φ_{a} field equation leads to an integration constant that breaks the global scale symmetry. We discuss the stabilizing effects of the coupling of the dilaton to the GB-topological density on the vacua with a very small cosmological constant and the resolution of the ‘TMT Vacuum-Manifold Problem’ which exists in the zero cosmological-constant vacuum limit. This problem generically arises from an effective potential that is a perfect square, and it gives rise to a vacuum manifold instead of a unique vacuum solution in the presence of many different scalars, like the dilaton, the Higgs, etc. In the non-zero cosmological-constant case this problem disappears. Furthermore, the GB coupling to the dilaton eliminates flat directions in the effective potential, and it totally lifts the vacuum-manifold degeneracy.

Original language | English |
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Article number | 240 |

Journal | European Physical Journal C |

Volume | 77 |

Issue number | 4 |

DOIs | |

State | Published - 1 Apr 2017 |

## ASJC Scopus subject areas

- Engineering (miscellaneous)
- Physics and Astronomy (miscellaneous)