Non-perturbative effects in field theory and gravity

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

Topological Model for Domain Walls in (Super-)Yang-Mills Theories

We derive a topological action that describes the confining phase of (Super-)Yang-Mills theories with gauge group $SU(N)$, similar to the work recently carried out by Seiberg and collaborators. It encodes all the Aharonov-Bohm phases of the possible non-local operators and phases generated by the intersection of flux tubes. Within this topological framework we show that the worldvolume theory of domain walls contains a Chern-Simons term at level $N$ also seen in string theory constructions. The discussion can also illuminate dynamical differences of domain walls in the supersymmetric and non-supersymmetric framework. Two further analogies, to string theory and the fractional quantum Hall effect might lead to additional possibilities to investigate the dynamics

Localization of gauge fields and Maxwell-Chern-Simons theory

We propose an explicit model, where an axionic domain wall dynamically localizes a U(1)-component of a nonabelian gauge theory living in a 3+1 dimensional bulk. The effective theory on the wall is 2+1d Maxwell-Chern-Simons theory with a compact U(1) gauge group. This setup allows us to understand all key properties of MCS theory in terms of the dynamics of the underlying 3+1 dimensional gauge theory. Our findings can also shed some light on branes in supersymmetric gluodynamics.Comment: 13 pages, 3 figure

Non-perturbative effects in field theory and gravity

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

Generative Temporal Models with Spatial Memory for Partially Observed Environments

In model-based reinforcement learning, generative and temporal models of environments can be leveraged to boost agent performance, either by tuning the agent's representations during training or via use as part of an explicit planning mechanism. However, their application in practice has been limited to simplistic environments, due to the difficulty of training such models in larger, potentially partially-observed and 3D environments. In this work we introduce a novel action-conditioned generative model of such challenging environments. The model features a non-parametric spatial memory system in which we store learned, disentangled representations of the environment. Low-dimensional spatial updates are computed using a state-space model that makes use of knowledge on the prior dynamics of the moving agent, and high-dimensional visual observations are modelled with a Variational Auto-Encoder. The result is a scalable architecture capable of performing coherent predictions over hundreds of time steps across a range of partially observed 2D and 3D environments.Comment: ICML 201