Flux Mixing and CP Violation in QCD

Abstract

We argue that kinetic mixing between topological flux sectors generates an effective shift of the QCD $\bar\theta$ angle, thereby inducing CP-violating effects. To demonstrate this mechanism, we analyze a $(1+1)$-dimensional $U(1)\times U(1)$ gauge theory as a controlled setting, where kinetic mixing leads to observable shifts in electric fluxes. We then extend the analysis to four dimensions using a three-form field description of QCD coupled to an additional $U(1)$ three-form gauge field. We find that hidden-sector fluxes, through kinetic mixing, shift the effective $\theta$ parameter of QCD and induce a nonzero expectation value of $\langle G\tilde{G}\rangle$. We discuss the implications for the strong CP problem and clarify under which conditions standard solutions, such as axion or CP/parity-based mechanisms, are compromised or remain robust.