Projective symmetries and induced electromagnetism in metric-affine gravity

TL;DR

This paper introduces a framework where projective symmetry in metric-affine gravity induces an effective electromagnetic coupling, linking the Dirac field with a U(1) gauge potential derived from non-metricity, resulting in an Einstein-Cartan-Maxwell theory with spinors.

Contribution

It demonstrates how projective symmetry can generate an effective electromagnetic field from non-metricity in metric-affine gravity, connecting gravity, spinors, and electromagnetism.

Findings

Effective U(1) gauge potential from non-metricity trace.

On-shell equivalence to Einstein-Cartan-Maxwell theory with Dirac fields.

Induction of electromagnetic interaction via projective symmetry.

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.