Emergent Solitons and the Philosophy of Non-Perturbative Quantum Field Theory

Solitons in quantum field theory are finite-energy solutions to the non-linear equations of motion. In this thesis, I argue that the solitons in two specific models, namely the sine-Gordon model and the Seiberg-Witten model, are emergent from dual models without solitons. Using the framework for emergence introduced by De Haro (2019), I argue that the behaviour in the sine-Gordon model fits the notion of epistemic emergence and that the behaviour in the Seiberg-Witten model fits the notion of ontological emergence. In these cases, a duality or an approximate duality serves as a linkage map between two models that contain some novelty with respect to each other. Contrary to the common relation between emergence and fundamentality in which a less fundamental theory emerges from a more fundamental theory, I argue that in these case studies, the emergent particle can be understood as equally fundamental as the elementary particle in the dual theory. This claim is made on an ontological level for the sine-Gordon model and on an epistemic level for the Seiberg-Witten model. Because soliton solutions are found by non-perturbative methods, an investigation of these models avoids many foundational problems related to perturbative renormalization, the method that is commonly used to treat
unphysical infinities that arise in quantum field theory. My claims are further substantiated by the fact that the particle spectra of the case studies can be computed exactly, which grants the models a mathematical rigour that is exceptional compared to other models formulated in Lagrangian quantum field theory.