The Origin of Spontaneous Symmetry Breaking in Theories with Large Extra Dimensions

We suggest that the Higgs particles can be identified with extra-dimensional components of the gauge fields, which after compactification on a certain topologically non-trivial (monopole) background become tachyonic and condense. The natural scale of the gauge symmetry breaking is set by an inverse radius of the internal space, which, in case of the electroweak symmetry, must be around $\sim 1/$TeV. 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 in 4-dimensions and in achieving spontaneous breaking of the 10-dimensional gauge group which we take to be $U(6)\times U(1)$, where U(1) couples only to gravity. We also work out the 4-dimensional effective action of a 6-dimensional theory with the gauge group SU(3). The effective 4-dimensional gauge symmetries are broken by Higgs type tachyons in the spectrum of the compcatified theories. We give a simple rule which helps us to identify the presence of such tachyons on the monopole background on $S^2$.