  We propose a new mechanism for generating a CP phase via Higgs a vacuum
expectation value originating from geometry of an extra dimension. A twisted
boundary condition is the key to produce an extra-dimension
coordinate-dependent vacuum expectation value, which contains a CP phase degree
of freedom and can be a new source of a CP phase in higher-dimensional gauge
theories. As an illustrative example, we apply our mechanism to a
five-dimensional gauge theory with point interactions and show that our
mechanism can dynamically produce a nontrivial CP-violating phase with
electroweak symmetry breaking, even though the five-dimensional model does not
include any CP-violating phases of Yukawa couplings in the five-dimensional
Lagrangian because of a single generation of five-dimensional fermions. We
apply our mechanism to a model with point interactions, which has no source of
CP-violating phases in the couplings of the higher-dimensional action, and show
that a nontrivial CP phase dynamically appears.
