Dimensional Crossover of Gauge Couplings on Orbifolds

We study the one-loop dimensional crossover effects in six-dimensional orbifold compactifications of N=1 supersymmetric gauge theories. The behaviour of the one-loop effective beta function and of the 4D effective gauge coupling are analysed for a wide range of momentum scales k relative to the compactification scale(s). As k is increasing and approaching the compactification scale(s), there exists a smooth transition (crossover) to a power-like behaviour of the 4D effective coupling, with a continuous one-loop beta function. The power-like behaviour sets in at momenta which are smaller than the compactification scale, to suggest a global effect of the Kaluza-Klein modes even below this scale. The experimental observation of such a behaviour is not necessarily a quantum “footprint” associated with the compactification, as usually thought, and is in general dominated by classical effects. Such power-like behaviour can be induced at the classical level by a higher derivative operator (with a suitable value for its tree level coupling) in any 4D effective theory (not necessarily derived from compactification). Special attention is paid to convergence issues near compactification scale(s) and to the scheme dependence of the results. E-mail Address: [email protected]