Alternative to Axions

Abstract

The $U(1)$ CP-violating phase which arises below chiral symmetry breaking in a non-Abelian gauge theory is ``secretly" the magnetic dual of the flux of a $U(1)$ $4$-form gauge field. Thus the discharge of this $4$-form flux by Schwinger production of charged membranes reduces the total CP-violating phase toward zero. This can safely restore CP symmetry to within the observational limits, $\theta_{\cancel{\tt CP}} \la 10^{-10}$, while also satisfying all limits from cosmology, when the charge and the tension of the gauge field sources are in the $\la keV$ range.