Topology and Volume Dependence in SU(N) Yang Mills Theories

In this dissertation we explore the interplay between volume and colour degrees offreedom in SU(N) Yang-Mills theories in various contexts. In particular, we study a finitevolume renormalization scheme that combines a gradient flow-based coupling, the useof twisted boundary conditions, and a special asymmetric geometry. We argue that thisscheme has several advantages that make it particularly suitable for precisiondeterminations of the strong coupling constant in QCD, and for extracting the Ndependence of the Λ parameter of SU(N) pure gauge theories. We test the schemenumerically by determining the Λ parameter for three values of N = 3, 5, and 8. The roleof topology and the influence of the volume in triggering topological fluctuations isdiscussed in detail. We explore the role of fractional charge instanton solutions in thissetup, and use numerical methods to study new SU(N) self-dual instanton-like solutionson R × T3 with fractional topological charge Q = 1/N.

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