QCD strings and the U(1) problem

We promote the usual QCD $\theta$-parameter to a field and interpret it as the phase of the quark condensate, which becomes nontrivial when topological defects, vortices in our formulation, are induced in the quark condensate by the QCD strings (chromoelectric flux tubes). The QCD topological term emerges naturally as a derivative coupling between the Chern-Simons current and a supercurrent in the quark condensate. This new formulation can address the $U_A(1)$ problem and leads to the chiral magnetic effects. It is possible that in this formulation the strong CP problem can be avoided without the axion particle.