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 grand unified theory scale, is unstable to the generation of hypercharge magnetic field. Quite large magnetic fields ( $\sim {10}^{22}$ G at $T\sim 100$ GeV with typical inhomogeneity scale $\sim \frac{{10}^6}{T}$) can be generated. These fields may be of cosmological interest, potentially acting as seeds for amplification to larger scale magnetic fields through nonlinear mechanisms. Previously derived bounds on exotic $B-L$ violating operators may also be evaded.