Six-dimensional gauge theory on the chiral square

We construct gauge theories in two extra dimensions compactified on thechiral square, which is a simple compactification that leads to chiral fermionsin four dimensions. Stationarity of the action on the boundary specifies theboundary conditions for gauge fields. Any six-dimensional gauge fielddecomposed in Kaluza-Klein modes includes a tower of heavy spin-1 particleswhose longitudinal polarizations are linear combinations of theextra-dimensional components, and a tower of heavy spin-0 particlescorresponding to the orthogonal combinations. These linear combinations dependon the Kaluza-Klein numbers, and are independent of the gauge fixing. If thegauge symmetry is broken by the vacuum expectation value of a six-dimensionalscalar, at each Kaluza-Klein level three spinless fields in the adjointrepresentation mix to provide the longitudinal polarization of the spin-1 mode,leaving the orthogonal states as two spin-0 particles. We derive theinteractions of the Kaluza-Klein modes for generic gauge theories, laying thegroundwork for the Standard Model in two universal extra dimensions, and moregenerally for future model building and phenomenological studies.Comment: 25 page