Pritzel, Alexander (2014): Non-perturbative effects in field theory and gravity. Dissertation, LMU München: Faculty of Physics
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### Abstract

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 theories 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 presence of this term was already conjectured in ealier works based on string theoretic constructions. Here we give its first purely field theoretical construction. Within this construction we also illuminate differences between domain walls in the supersymmetric and non-supersymmetric case.\\ Lastly we try to relate the effects observed to similar effects in critical string theories and we also speculate on whether the behaviour of these domain walls is due to an analog of the fractional quantum hall effect.\\ In the second part of this thesis we investigate non-perturbative aspects of black hole physics. Here we consider a model for a low energy description of black holes due to Dvali and Gomez, where black holes are described in terms of a Bose-Einstein condensate (BEC) of weakly interacting gravitons near a quantum critical point. We focus on nonperturbative properties of a system of attractively self-interacting non-relativistic bosons, which was proposed as a toy model for graviton BECs by Dvali and Gomez. In this thesis we investigate this system mostly relying on a fully non-perturbative approach called exact diagonalization. We first investigate entanglement properties of the ground state of the system, showing that the ground state becomes strongly entangled as one approaches the quantum critical point. In order to make this notion precise we introduce the notion of fluctuation entanglement. We then compute it in a Bogoliubov analysis and extract it from the exact diagonlization procedure as well. We also consider the real time evolution of the system. Here we are interested in finding an analog of the conjectured fast scrambling property of black holes originally introduced by Hayden and Preskill. We only consider the weaker notion of quantum breaking and show that the toy model has a quantum break time consistent with the fast scrambling time scale conjectured in the black hole context. We then conclude by pointing out several possible extensions of these results.