Projective symmetries and induced electromagnetism in metric-affine gravity

Abstract

We present a framework in which the projective symmetry of the Einstein-Hilbert action in metric-affine gravity is used to induce an effective coupling between the Dirac lagrangian and the Maxwell field. The effective $U(1)$ gauge potential arises as the trace of the non-metricity tensor $Q_{\mu a}{}^a$ and couples in the appropriate way to the Dirac fields to in order to allow for local phase shifts. On shell, the obtained theory is equivalent to Einstein-Cartan-Maxwell theory in presence of Dirac spinors.

arXiv comment6 pages, no figures. v2: Minor changes, references added. Version to be published in Phys. Lett. B

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Cited by in corpus (4)

• Cosmology in $f(Q)$ geometry
• Scale transformations in metric-affine geometry
• Minimal coupling in presence of non-metricity and torsion
• A modified gravity model coupled to a Dirac field in 2D spacetimes with quadratic nonmetricity and curvature