Mariani, Alessandro (2024). Abelian lattice gauge theories in three dimensions. (Thesis). Universität Bern, Bern

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Abstract

Lattice gauge theories in three spacetime dimensions are relevant for condensed matter physics, but also as a testbed for ideas in particle physics. Here we focus on pure gauge theories without matter, which, especially in the Abelian case, are often thought to be less interesting; in this work we hope to demonstrate that they display a very rich physics. The first theory that we consider is the non-compact integer-valued gauge theory whose gauge group is Z. This is relevant for the study of vortices, topological excitations which are found in superfluids. We consider the problem of their construction in a fully quantum theory. Our novel result is the numerical calculation of a set of critical exponents associated to the vortices as well as the demonstration that they obey a simple scaling relation. We then consider the compact gauge theory whose gauge group is U(1). We review the well-known literature on this topic, as well as the celebrated proof of confinement in this theory. Our novel contribution is the numerical calculation of its equation of state at finite temperature. It allows us to probe the spectrum of the theory and discuss some of the peculiar features of confinement in this theory, such as the existence of inequivalent length scales as well as its effective description as a scalar theory. Finally, we consider a novel modification of the U(1) gauge theory which can be constructed by introducing a topological angle α. This is most natural in the Hamiltonian formalism. We compute several quantities in the case α = π, and show that this theory displays quite unusual properties for a gauge theory, such as a broken Z2 symmetry in the continuum limit as well as fractionalized flux strings.

Item Type:	Thesis
Dissertation Type:	Single
Date of Defense:	3 July 2024
Subjects:	500 Science > 530 Physics
Institute / Center:	08 Faculty of Science > Institute of Theoretical Physics 10 Strategic Research Centers > Albert Einstein Center for Fundamental Physics (AEC)
Depositing User:	Hammer Igor
Date Deposited:	11 Jul 2024 11:29
Last Modified:	12 Jul 2024 02:05
URI:	https://boristheses.unibe.ch/id/eprint/5201

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