  We suggest that the electroweak Higgs particles can be identified with
extra-dimensional components of the gauge fields, which after compactification
on a certain topologically non-trivial background become tachyonic and
condense. If the tachyonic mass is a tree level effect, the natural scale of
the gauge symmetry breaking is set by the inverse radius of the internal space,
which, in case of the electroweak symmetry, must be around $\sim 1/$TeV. We
discuss the possibility of a vanishing tree level mass for the Higgs. In such a
scenario the tachyonic mass can be induced by quantum loops and can be
naturally smaller than the compactification scale. We give an example in which
this possibility can be realized. Starting from an Einstein--Yang--Mills theory
coupled to fermions in 10-dimensions, we are able to reproduce the spectrum of
the Standard Model like chiral fermions and Higgs type scalars in 4-dimensions
upon compactifying on ${\mathbb{C}}P^1\times {\mathbb{C}}P^2$. The existence of
a monopole solution on ${\mathbb{C}}P^1$ and a self dual U(1) instanton on
${\mathbb{C}}P^2$ are essential in obtaining chiral fermions as well as
tachyonic or massless scalars in 4-dimensions. We give a simple rule which
helps us to identify the presence of tachyons on the monopole background on
$S^2$.
