Origin of spontaneous symmetry breaking in theories with large extra dimensions

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 nontrivial 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 the case of electroweak symmetry, must be around ∼1/TeV. We discuss the possibility of a vanishing tree level mass for the Higgs boson. 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 ten dimensions, we are able to reproduce the spectrum of the standard model, such as chiral fermions and Higgs type scalars, in four dimensions upon compactifying on $C{P}^1\times C{P}^2.$ The existence of a monopole solution on $C{P}^1$ and a self-dual U(1) instanton on $C{P}^2$ is essential in obtaining chiral fermions as well as tachyonic or massless scalars in four dimensions. We give a simple rule that helps us to identify the presence of tachyons on the monopole background on $S^2.$