Chiral Compactification on a Square

TL;DR

This paper explores a six-dimensional quantum field theory compactified on a square with specific boundary conditions, leading to chiral fermions and symmetries akin to a T^2/Z_4 orbifold, with implications for particle stability.

Contribution

It introduces a novel boundary condition for compactification on a square that yields chiral fermions and exact symmetries in four dimensions, connecting to orbifold models.

Findings

Nontrivial solutions exist only for phases multiple of π/2.

Compactification is equivalent to a T^2/Z_4 orbifold.

Exact Z_8×Z_2 symmetry ensures particle stability.

Abstract

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.