LAUSR

Asymptotic freedom is comprehensively studied in the context of universal extra dimensions. The use of a ${\rm SU}(N)$-covariant gauge-fixing procedure to quantize the theory is stressed. One-loop contributions of Kaluza-Klein (KK) excitations are characterized by discrete KK sums and continuous momenta sums, so two types of ultraviolet divergences are identified, one arising from poles of the gamma function and associated with short-distance effects in the usual 4-dimensional spacetime manifold, and the other emerging from poles of the 1-dimensional Epstein function and corresponding to short-distance effects in the compact manifold. We address the cases of 5 and $4+n$ dimensions ($n \geq2$) separately. In 5 dimensions the 1-dimensional Epstein function is convergent, so the usual counterterm renormalizes the vacuum polarization function. For $4+n$ dimensions, the 1-dimensional Epstein function is divergent, so renormalization in a modern sense is implemented by interactions of canonical dimension higher than 4, already present in the effective theory. The polarization function is renormalized using both a mass-dependent scheme and a mass-independent scheme, with extra-dimensions effects decoupling in the former case but not in the latter. The beta function is calculated for an arbitrary number of extra dimensions. We emphasize the advantages of a mass-dependent scheme in this type of theories, in which decoupling is manifest. Asymptotic freedom is reinforced by the contributions from KK excited modes of Yang-Mills fields.