Abstract
We propose a way towards a dynamical solution of the strong $CP$ in models with compact extra dimensions. To this aim we consider a one dimensional toy model for QCD, which contains a vacuum angle and a strong $CP$-like problem. We further consider a higher dimensional theory, which has a trivial vacuum structure and which reproduces the perturbative properties of the toy model in the low-energy limit. In the weak coupling regime, where our computations are valid, we show that the vacuum structure of the low-energy action is still trivial and the strong $CP$ problem does not arise. Also, no axionlike particles are generated in this setup.
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