Schubring, Daniel2022-09-262022-09-262022-07https://hdl.handle.net/11299/241710University of Minnesota Ph.D. dissertation. 2022. Major: Physics. Advisor: Mikhail Shifman. 1 computer file (PDF); 192 pages.Various aspects of non-linear sigma models with an SU(N) x U(1) symmetric target space are considered. In the case N=2, three-dimensional topological defects are discussed which are relevant for frustrated magnetic systems and which may offer a new perspective on the Skyrme model. An apparent discrepancy between the large N expansion and the weak coupling expansion noted earlier in the literature is reviewed and clarified. A systematic approach to the operator product expansion at sub-leading order in large N is developed and the spinon two-point function is expanded as a trans-series in which all ambiguities in the Borel plane are shown to cancel.enCondensed matter physicsHigh energy physicsTheoretical physicsThesis or Dissertation