  We present some interesting connections between $PT$ symmetry and conformal
symmetry. We use them to develop a metricated theory of electromagnetism in
which the electromagnetic field is present in the geometric connection.
However, unlike Weyl who first advanced this possibility, we do not take the
connection to be real but to instead be $PT$ symmetric, with it being
$iA_{\mu}$ rather than $A_{\mu}$ itself that then appears in the connection.
With this modification the standard minimal coupling of electromagnetism to
fermions is obtained. Through the use of torsion we obtain a metricated theory
of electromagnetism that treats its electric and magnetic sectors
symmetrically, with a conformal invariant theory of gravity being found to
emerge. An extension to the non-Abelian case is provided.
