Primordial Magnetic Fields, Right Electrons, and the Abelian Anomaly

In the standard model there are charges with abelian anomaly only (e.g. right-handed electron number) which are effectively conserved in the early universe until some time shortly before the electroweak scale. A state at finite chemical potential of such a charge, possibly arising due to asymmetries produced at the GUT scale, is unstable to the generation of hypercharge magnetic field. We argue that quite large magnetic fields ($\sim 10^{23}$ gauss at $T\sim 3$ TeV with typical inhomogeneity scale up to $\sim interest, potentially acting as seeds for amplification to larger scale magnetic fields through non-linear mechanisms.