Unitarity of compactified five-dimensional Yang–Mills theory

Compactified five-dimensional Yang–Mills theory results in an effective four-dimensional theory with a Kaluza–Klein (KK) tower of massive vector bosons. We explicitly demonstrate that the scattering of the massive vector bosons is unitary at tree-level for low energies, and analyze the relationship between the unitarity violation scale in the KK theory and the nonrenormalizability scale in the five-dimensional gauge theory. In the compactified theory, low-energy unitarity is ensured through an interlacing cancellation among contributions from the relevant KK levels. Such cancellations can be understood using a Kaluza–Klein equivalence theorem which results from the geometric “Higgs” mechanism of compactification. In these theories, the unitarity violation is delayed to energy scales higher than the customary limit through the introduction of additional vector bosons rather than Higgs scalars.