Abstract
We note that orbifold boundary conditions that produce chiral fermion zero modes in compactified higher dimensional theories may distort scalar field vacuum expectation values, giving rise to nontrivial dependence on the extra dimensions. We illustrate this in a simple five dimensional model which has chiral fermion zero-modes stuck to fat branes. The model could provide a simple and explicit realization of the separation of quarks and leptons in the fifth dimension. We discuss the KK expansion in some detail. We find that there are in general non-zero-mode states stuck to the brane, like the chiral zero modes. We see explicitly the transition from states dominated by the internal structure of the fat brane to those dominated by the compactification.
Highlights
We note that orbifold boundary conditions that produce chiral fermion zero modes in compactified higher dimensional theories may distort scalar field vacuum expectation values, giving rise to nontrivial dependence on the extra dimensions
It may even be relevant if the extra dimensions are infinite, if the gravitational interactions distort the extra dimensions in an appropriate way [3]
The generic result is a pair of fat branes with a highly nontrivial structure in the fifth dimension whose consequences we explore in the rest of the paper
Summary
A field theory in a space of more than four space-time dimensions may be relevant to the description of the real world if the extra dimensions are compactified [1, 2]. (1.4) is equivalent to having the chiral fields defined on a circle, x5 ∈ [0, 2L) with 2L identified with 0, but with the chiral components ψ± required to be respectively symmetric and antisymmetric at the fixed-points x5 = 0 and x5 = L, so this is an S1/Z2 orbifold [6] This simple model has a chiral fermion zero-mode, ψ+(x, x5) = ψ(x) , ψ−(x, x5) = 0 ,. This simple model has a chiral zero-mode that is uniformly spread over the compact extra dimension. Using techniques borrowed from supersymmetric quantum mechanics [7], we construct many of the KK modes in detail and identify qualitative features that depend on the nontrivial structure in the extra dimension
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