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Karananas, Georgios K.; Shaposhnikov, Mikhail; Shkerin, Andrey and Zell, Sebastian (2021): Scale and Weyl invariance in Einstein-Cartan gravity. In: Physical Review D, Vol. 104, No. 12, 124014

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We show how Einstein-Cartan gravity can accommodate both global scale and local scale (Weyl) invariance. To this end, we construct a wide class of models with nonpropagating torsion and a nonminimally coupled scalar field. In phenomenological applications the scalar field is associated with the Higgs boson. For global scale invariance, an additional field-dilaton-is needed to make the theory phenomenologically viable. In the case of the Weyl symmetry, the dilaton is spurious and the theory reduces to a subclass of one-field models. In both scenarios of scale invariance, we derive an equivalent metric theory and discuss possible implications for phenomenology.

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