  Free massless scalars have a shift symmetry. This is usually broken by gauge
and Yukawa interactions, such that quantum corrections induce a quadratically
divergent mass term. In the Standard Model this leads to the hierarchy problem
of the electroweak theory, the question why the Higgs mass is so much smaller
than the Planck mass. We present an example where a large scalar mass term is
avoided by coupling the scalar to an infinite tower of massive states which are
obtained from a six-dimensional theory compactified on a torus with magnetic
flux. The series of divergent quantum corrections adds up to zero, and we show
explicitly that the shift symmetry of the scalar is preserved in the effective
four-dimensional theory despite the presence of gauge and Yukawa interaction
terms.
