Primordial Galactic Magnetic Fields from Domain Walls at the QCD Phase Transition

We propose a mechanism to generate large-scale magnetic fields with correlation lengths of 100 kpc. Domain walls with QCD-scale internal structure form and coalesce, obtaining Hubble-scale correlations while aligning nucleon spins. Because of strong $\mathrm{CP}$ violation, the walls are ferromagnetic, which induces electromagnetic fields with Hubble-size correlations. The $\mathrm{CP}$ violation also induces a maximal helicity (Chern-Simons) which supports an “inverse cascade,” allowing the initial correlations to grow to 100 kpc today. We estimate the generated electromagnetic fields in terms of the QCD parameters and discuss the effects of the resulting fields.