Six-Dimensional Gauge Theory on the Chiral Square
  We construct gauge theories in two extra dimensions compactified on the chiral square, which is a simple compactification that leads to chiral fermions in four dimensions. Stationarity of the action on the boundary specifies the boundary conditions for gauge fields. Any six-dimensional gauge field decomposed in Kaluza-Klein modes includes a tower of heavy spin-1 particles whose longitudinal polarizations are linear combinations of the extra-dimensional components, and a tower of heavy spin-0 particles corresponding to the orthogonal combinations. These linear combinations depend on the Kaluza-Klein numbers, and are independent of the gauge fixing. If the gauge symmetry is broken by the vacuum expectation value of a six-dimensional scalar, at each Kaluza-Klein level three spinless fields in the adjoint representation mix to provide the longitudinal polarization of the spin-1 mode, leaving the orthogonal states as two spin-0 particles. We derive the interactions of the Kaluza-Klein modes for generic gauge theories, laying the groundwork for the Standard Model in two universal extra dimensions, and more generally for future model building and phenomenological studies. 
Gustavo Burdman, Bogdan A. Dobrescu and Eduardo Ponton