Yang-Mills theories with an arbitrary number of compactified extra dimensions

Abstract

The well-known Yang-Mills theory with one $ S^{1} / Z_{2}$ universal extra dimension (UED) is generalized to an arbitrary number of spatial extra dimensions through a novel compactification scheme. In this paper, the Riemannian flat based manifold under consideration contains $ n $ spatial extra dimensions defined by $ n $ copies of the orbifold $ S^{1} / Z_{2}$. In this approach, we present the gauge structure and the mass spectrum of the effective four-dimensional theory. We introduce the concept of standard and nonstandard gauge transformations of the effective theory, and explicitly identify the emergence of massive vector fields in the same number as massless ('pseudo-Goldstone') scalars in the compactified theory, verifying that a Higgs-like mechanism operates in the compactification process. It is found that, in contrast with the one UED scenario, in cases with two or more UEDs there emerge massive scalar fields. Besides, at phase-space level, the Hamiltonian analysis yields that the higher-dimensional and compactified theories are classically equivalent using the fundamental concept of canonical transformation. This work lays the ground for a wider study on these theories concerning their quantization and predictive power at the level of quantum fluctuations.