Nonperturbative effects are crucial to fully understand the dynamics of quantum field theories including important topics such as confinement or black hole evaporation. In this thesis we investigate two systems where nonperturbative effects are of paramount importance. In the first part we study the dynamics of non-abelian gauge theories, while in the second part we try to shed light on mysterious properties of black holes using a model proposed earlier by Dvali and Gomez.\\ Non-abelian gauge

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... eories are the central element in the standard model of particle physics and many dynamical aspects remain elusive. $\mathcal{N}=1$ supersymmetric Yang-Mills theories with $SU(N_C)$ allows for domain walls with several curious properties. They are expected to have gauge fields with a Chern-Simons (CS) term living on their worldvolume, while in the 't Hooft limit of a large number of colors many of their properties seem reminiscent of string theoretic D-Branes. Similar domain walls were also conjectured to be present in non supersymmetric Yang Mills theories. In our work, we investigate this problem from several points of view. We construct a toy model of how to localize a gauge field with a CS term on a domain wall extending earlier work by Dvali and Shifman. We then derive the peculiar properties of CS terms in terms of effects of the underlying microscopic dynamics. Then we look at the actual theory of interest. Here the main novelty is the focus on the topological part of the Yang-Mills theory allowing us to make robust statements despite working in a strongly coupled theory. We construct the low energy effective action of both the non-supersymmetric as well as the supersymmetric Yang Mills theory, which due to the presence of a mass gap is a topological field theory. This topological field theory encodes the Aharanov-Bohm phases in the theory as well as phases due to intersection of flux tubes. In this topological field theory we see that the worldvolume theory of domain walls contains a level $N_C$ CS term. The presen [...]