Gauging Away the Strong CP Problem

We propose a new solution to the strong-CP problem. It involves the existence of an unbroken gauged $U(1{)}_X$ symmetry whose gauge boson gets a Stuckelberg mass term by combining with a pseudoscalar field $\eta (x)$. The latter has axion-like couplings to $F_{QCD}\wedge F_{QCD}$ so that the theta parameter may be gauged away by a $U(1{)}_X$ gauge transformation. This system leads to mixed gauge anomalies and we argue that they are cancelled by the addition of an appropriate Wess-Zumino term, so that no SM fermions need to be charged under $U(1{)}_X$. We discuss scenarios in which the above set of fields and couplings appear. The mechanism is quite generic, but a natural possibility is that the the $U(1{)}_X$ symmetry arises from bulk gauge bosons in theories with extra dimensions or string models. We show that in certain D-brane Type-II string models (with antisymmetric tensor field strength fluxes) higher dimensional Chern-Simons couplings give rise to the required D=4 Wess-Zumino terms upon compactification. In one of the possible string realizations of the mechanism the $U(1{)}_X$ gauge boson comes from the Kaluza-Klein reduction of the eleven-dimensional metric in M-theory.