Primordial helical magnetic fields from inflation?

We revisit the mechanism of helical magnetogenesis during inflation with a parity-violating interaction using the formalism of stochastic inflation. One of the polarizations of the gauge field undergoes tachyonic growth, leading to the generation of helical magnetic fields. We obtain the Langevin equations associated with the electromagnetic fields, which are in the form of Ornstein-Uhlenbeck stochastic differential equations. Consequently, the tachyonic growth of the helical magnetic fields is balanced by a meanreverting process of stochastic dynamics such that the magnetic fields settle down to an equilibrium state with the amplitude smaller than what is obtained in the absence of the stochastic noises. Working in the parameter space of the model where both the backreaction and the strong coupling problems are under control, the model does not provide a large enough seed to be amplified by the galactic dynamo as the source of the magnetic fields observed on cosmological scales.