  We argue that the necessity of picking an imaginary time direction for the
analytic continuation to Minkowski signature gives a new point of view on the
problem of Euclidean spinor fields, allowing an interpretation in Minkowski
space-time of one of the chiral factors of Spin(4)=SU(2)xSU(2) as an internal
symmetry. The imaginary time direction spontaneously breaks this SU(2), playing
the role of the Higgs Field. Twistor geometry provides a compelling framework
for formulating spinor fields in complexified four-dimensional space-time and
implementing the above suggestion. Projective twistor space PT naturally
includes an internal SU(3) symmetry as well as the above SU(2), and spinors on
this space behave like a generation of leptons. Since only one chirality of the
Euclidean Spin(4) is a space-time symmetry after analytic continuation and the
Higgs field defines the imaginary time direction, the space-time geometry
degrees of freedom are only a chiral SU(2) connection and a spatial frame.
These may allow a consistent quantization of gravity in a chiral formulation,
unified in the twistor framework with the degrees of freedom of the Standard
Model. This unification proposal is incomplete, still requiring implementation
as a theory with gauge symmetry on PT, perhaps related to known correspondences
between super Yang-Mills theories and supersymmetric holomorphic Chern-Simons
theories on PT.
