M. A. López-Osorio, E. Martínez-Pascual, H. Novales-Sánchez, J. J. Toscano
In a previous paper by some of us (arXiv:1008.4638v2 [hep-ph]), the gauge structure of Yang-Mills theories with one universal extra dimension was explored. In particular, two types of gauge invariance were identified and classified as standard gauge transformations (SGT) and nonstandard gauge transformations (NSGT). The main purpose of this work is to give a precise meaning to this classification within the context of hidden symmetries. In three different gauge systems, suitable canonical transformations capable of hiding explicit symmetries are found. The systems under consideration are: (i) four dimensional pure SU(3) Yang-Mills theory, (ii) four dimensional SU(3) Yang-Mills with spontaneous symmetry breaking, and (iii) pure Yang-Mills theory with one universal compact extra dimension. In all cases the original system is mapped into a certain effective theory that is invariant under the so-called SGT and NSGT. In the case where spontaneous symmetry breaking is present, the set of SGT corresponds to the group to which the original gauge group is broken into, whereas the NSGT are associated to the broken generators. System (ii) is a particular case of the more general scenario in which the symmetry G is broken into H and a canonical transformation is introduced to map covariant objects under G into covariant objects under H. For systems (i) and (ii) the group of SGT is SU(2), whereas for the system (iii) this group is referred to as SU(N,\mc{M}^{4}), the standard SU(N) with gauge parameters defined on four dimensional Minkowski spacetime. Prospects to generalize the system (iii) to more than one extra dimension are also discussed. The differences between the pseudo-Goldstone bosons that emerge from a degenerate vacuum and those induced by compactification are stressed.
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http://arxiv.org/abs/1302.2981
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