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 ex...

We give a definition of character sheaves on the group compactification which is equivalent to Lusztig’s definition in [Moscow Math. J. 4 (2004) 869-896]. We also prove some properties of the character sheaves on the group compactification.