Hidden symmetries induced by a canonical transformation and gauge structure of compactified Yang-Mills theories

Abstract

Compactified Yang-Mills theories with one universal extra dimension were found [arXiv:1008.4638] to exhibit two types of gauge invariances: the standard gauge transformations (SGTs) and the nonstandard gauge transformations (NSGTs). In the present work we show that these transformations are not exclusive to compactified scenarios. Introducing a notion of hidden symmetry, based on the fundamental concept of canonical transformation, we analyse three different gauge systems, each of which is mapped to a certain effective theory that is invariant under the so-called SGTs and NSGTs. The systems under discussion 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. The canonical transformation, that induces the notion of hidden symmetry, maps objects with well defined transformation laws under a gauge group $G$ to well defined objects under a non-trivial subgroup $H\subset G$. In the case where spontaneous symmetry breaking is present, the set of SGTs corresponds to the group into which the original gauge group is broken into, whereas the NSGTs are associated to the broken generators and can be used to define the unitary gauge. For the system (iii), the SGTs coincide with the gauge group $SU(N,{\mathcal{M}}^4)$, whereas the NSGTs do not form a group; in this system the 'fundamental' theory and the effective one are shown to be classically equivalent.

26 pages, title has changed, some comments and clarifications added, some references added

References in corpus (18)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Dark Matter and Collider Phenomenology of Universal Extra Dimensions
• Relic abundance of dark matter in the minimal universal extra dimension model
• Exotic Collider Signals from the Complete Phase Diagram of Minimal Universal Extra Dimensions
• Testing Minimal Universal Extra Dimensions Using Higgs Boson Searches at the LHC
• Search for the minimal universal extra dimension model at the LHC with $\sqrt{s}$=7 TeV
• Universal Extra-Dimensional models with boundary localized kinetic terms: Probing at the LHC
• Relic abundance of dark matter in universal extra dimension models with right-handed neutrinos
• Production of Higgs boson excitations of universal extra dimension at the Large Hadron Collider
• Solving cosmological problem in universal extra dimension models by introducing Dirac neutrino
• Gauge invariance and quantization of Yang-Mills theories in extra dimensions
• Universal Extra Dimensions, Radiative Returns and the Inverse Problem at a Linear e+e- Collider
• Productions of second Kaluza-Klein gauge bosons in the minimal universal extra dimension model at LHC
• Bilepton effects on the WWV^* vertex in the 331 model with right-handed neutrinos via a SU_L(2)XU_Y(1) covariant quantization scheme
• One-loop effects of extra dimensions on the WWγand WWZ vertices
• Dependence of SU(N) coupling behavior on the size of extra dimensions
• Direct bound on the minimal Universal Extra Dimension model from the $t\bar{t}$ resonance search at the Tevatron

Cited by in corpus (6)

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• Yang-Mills theories with an arbitrary number of compactified extra dimensions
• Distinctive ultraviolet structure of extra-dimensional Yang-Mills theories by integration of heavy Kaluza-Klein modes
• Effects of universal extra dimensions on top-quark electromagnetic interactions
• Gauge-invariant approach to the beta function in Yang-Mills theories with universal extra dimensions
• Gauge structure of Yang-Mills theories with extra dimensions