Integration of Kaluza-Klein modes in Yang-Mills theories

Abstract

A five dimensional pure Yang--Mills theory, with the fifth coordinate compactified on the orbifold $S^1/Z_2$ of radius R, leads to a four dimensional theory which is governed by two types of local gauge transformations, namely, the well known standard gauge transformations (SGT) dictated by the $S{U}_4(N)$ group under which the zero Fourier modes transform as gauge fields, and a set of nonstandard gauge transformations (NSGT) determining the gauge nature of the Kaluza--Klein (KK) excitations. By using a SGT-covariant gauge-fixing procedure for removing the degeneration associated with the NSGT, we integrate out the KK excitations and obtain a low-energy effective Lagrangian expansion involving all of the independent canonical-dimension-six operators that are invariant under the SGT of the $S{U}_4(N)$ group and that are constituted by light gauge fields (zero modes), exclusively. It is shown that this effective Lagrangian is invariant under the SGT, but it depends on the gauge-fixing of the gauge KK excitations. Our result shows explicitly that the one-loop contributions of the KK excitations to light (standard) Green's functions are renormalizable.

17 pages, a new paragraph and some new equations were added

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Cited by in corpus (8)

• Trilinear gauge boson couplings in the standard model with one universal extra dimension
• Hidden symmetries induced by a canonical transformation and gauge structure of compactified Yang-Mills theories
• 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
• Gauge-invariant approach to the beta function in Yang-Mills theories with universal extra dimensions
• The Standard Model with one universal extra dimension
• Diphoton Higgs signal strength in universal extra dimensions
• Gauge invariance, quantization and integration of heavy modes in a gauge Kaluza-Klein theory