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Title: Topological Structures in Supersymmetric Gauge Theories
Authors: Fan, Yale
Advisors: Pufu, Silviu S.
Contributors: Physics Department
Subjects: Physics
Issue Date: 2020
Publisher: Princeton, NJ : Princeton University
Abstract: This thesis explores the nonperturbative physics of three-dimensional gauge field theories with varying amounts of supersymmetry through an analysis of their one-dimensional topological substructures. In the setting of four supercharges, we consider the topological quantum mechanics of Wilson lines in pure Chern-Simons theory. We reframe the perturbative renormalization of observables in this theory in terms of a localization principle associated with an underlying N = 2 supersymmetry. This perspective allows the otherwise perturbative corrections to be interpreted as nonperturbative consequences of a non-renormalization theorem. In the setting of eight supercharges, we develop an approach to the study of Coulomb branch operators in 3D N = 4 gauge theories and the deformation quantization of their Coulomb branches. To do so, we leverage the existence of a 1D topological subsector whose operator product expansion takes the form of an associative and noncommutative algebra on the Coulomb branch. For "good" and "ugly" theories in the Gaiotto-Witten classification, we exhibit a trace map on this algebra, which amounts to a procedure for computing exact correlation functions of a class of local operators, including certain monopole operators, on S^3. We introduce a "shift operator" formalism for constructing correlators on S^3 by gluing hemispheres HS^3, and we show how to recover our results by dimensionally reducing the line defect Schur index of 4D N = 2 gauge theories. We use our results to study 3D mirror symmetry and to characterize monopole bubbling effects in nonabelian gauge theories. In the process, we arrive at a physical proof of the Bullimore-Dimofte-Gaiotto abelianization description of the Coulomb branch.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog:
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Physics

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