Phase of Quark Condensate and Topological Current in QCD

We propose a new topological charge term in QCD based on flux-tube models. It couples a superflow of the phase of the quark condensate to the Chern-Simons current. The usual $\theta$-parameter is replaced by the phase of the quark condensate, which becomes nontrivial due to the existence of topological defects such as vortices. This new formulation can address the U(1) problem in a similar way as in the $\theta$-world and may avoid the strong CP problem as the new topological charge term is a derivative coupling. Some phenomenological applications like chiral magnetic effects and possible connections to the Josephson effect are discussed.