Chiral Compactification on a Square

Details Chiral Compactification on a Square Chiral Compactification on a Square

2004-01-07

arxiv.org/abs/hep-th/0401032v2

JHEP 0403 (2004) 071

Physics

High Energy Physics

High Energy Physics - Theory

28 pages, latex. References added. Clarifying remarks included in section 2. Minor corrections made in section 3

Scientific paper

10.1088/1126-6708/2004/03/071

We study quantum field theory in six dimensions with two of them compactified on a square. A simple boundary condition is the identification of two pairs of adjacent sides of the square such that the values of a field at two identified points differ by an arbitrary phase. This allows a chiral fermion content for the four-dimensional theory obtained after integrating over the square. We find that nontrivial solutions for the field equations exist only when the phase is a multiple of \pi/2, so that this compactification turns out to be equivalent to a T^2/Z_4 orbifold associated with toroidal boundary conditions that are either periodic or anti-periodic. The equality of the Lagrangian densities at the identified points in conjunction with six-dimensional Lorentz invariance leads to an exact Z_8\times Z_2 symmetry, where the Z_2 parity ensures the stability of the lightest Kaluza-Klein particle.

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