  Einstein-Cartan theory is an extension of the standard formulation of General
Relativity where torsion (the antisymmetric part of the affine connection) is
non-vanishing. Just as the space-time metric is sourced by the stress-energy
tensor of the matter fields, torsion is sourced via the spin density tensor,
whose physical effects become relevant at very high spin densities. In this
work we introduce an extension of the Einstein-Cartan-Dirac theory with an
electromagnetic (Maxwell) contribution minimally coupled to torsion. This
contribution breaks the $U(1)$ gauge symmetry, which is suggested by the
possibility of a torsion-induced phase transition in the early Universe,
yielding new physics in extreme (spin) density regimes. We obtain the
generalized gravitational, electromagnetic and fermionic field equations for
this theory, estimate the strength of the corrections, and discuss the
corresponding phenomenology. In particular, we briefly address some
astrophysical considerations regarding the relevance of the effects which might
take place inside ultra-dense neutron stars with strong magnetic fields
(magnetars).
