Gravitational Coleman-Weinberg mechanism

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The Coleman-Weinberg mechanism provides a procedure by which a scalar field, which initially has no mass parameters, acquires a mass due to the anomalous nature of scale symmetry. Loop corrections trigger a spontaneous symmetry breaking and the appearance of a non-trivial vacuum. We first review the basic example of the Coleman-Weinberg mechanism, scalar Quantum Electrodynamics, in a perturbative regime where the scalar particle becomes massive through photon loops. We then present the main results of this article, what we name the gravitational Coleman-Weinberg mechanism: we analyse the same effect in a gravitational theory without explicit energy scales at tree-level. Finally, we also study the mechanism for two scalar fields in the mentioned gravitational theory. We will derive the gravitational Coleman-Weinberg potentials, analyse the parameter space where we have a symmetry breaking, and obtain the value of the corresponding scalar masses.
© 2023 The Authors. This work was supported by Grants FPU16/06960 (MECD), the MICINN (Spain) project PID2019-107394GB-I00/AEI/10.13039/501100011033 (AEI/FEDER, UE), and PID2019-108655GB-I00/AEI/10.13039/501100011033, UCM under research group 910309, IPAR-COS institute, and by EU STRONG-2020 under the program H2020-INFRAIA-2018-1 [grant no. 824093]. JARC acknowledges support by Institut Pascal at Universite Paris-Saclay during the Paris-Saclay Astroparticle Symposium 2022, with the support of the P2IO Laboratory of Excellence (program "Investissements d'avenir" ANR-11-IDEX-0003-01 Paris-Saclay and ANR-10-LABX-0038), the P2I axis of the Graduate School of Physics of Universite Paris-Saclay, as well as IJCLab, CEA, APPEC, IAS, OSUPS, and the IN2P3 master projet UCMN. Part of the contribution of JARC to this article is based upon work from COST Action COSMIC WISPers CA21106, supported by COST (European Cooper-ation in Science and Technology).
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