The 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 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 $S^2$.Comment: 33 pages. Version accepted for publication in Phys.Rev.

Baryogenesis vs. proton stability in theories with extra dimensions

We propose a new scenario of baryogenesis in the context of theories with large extra dimensions. The baryon number is almost conserved at zero temperature by means of a localization mechanism recently analyzed by Arkani-Hamed and Schmaltz: leptons and quarks are located at two slightly displaced positions in the extra space, and this naturally suppresses the interactions which ``convert'' the latter in the former. We show that this is expected to be no longer true when finite temperature effects are taken into account. The whole scenario is first presented in its generality, without referring to the bulk geometry or to the specific mechanism which may generate the baryon asymmetry. As an example, we then focus on a baryogenesis model reminiscent of GUT baryogenesis. The Sakharov out of equilibrium condition is satisfied by assuming nonthermal production of the bosons that induce baryon number violation.Comment: 10 pages, 1 figur