Can slow roll inflation induce relevant helical magnetic fields?
  We study the generation of helical magnetic fields during single field
inflation induced by an axial coupling of the electromagnetic field to the
inflaton. During slow roll inflation, we find that such a coupling always leads
to a blue spectrum with $B^2(k) \propto k$, as long as the theory is treated
perturbatively. The magnetic energy density at the end of inflation is found to
be typically too small to backreact on the background dynamics of the inflaton.
We also show that a short deviation from slow roll does not result in strong
modifications to the shape of the spectrum. We calculate the evolution of the
correlation length and the field amplitude during the inverse cascade and
viscous damping of the helical magnetic field in the radiation era after
inflation. We conclude that except for low scale inflation with very strong
coupling, the magnetic fields generated by such an axial coupling in single
field slow roll inflation with perturbative coupling to the inflaton are too
weak to provide the seeds for the observed fields in galaxies and clusters.
