Non-Invertible Symmetry in Lower Dimensional Gauge Theory

This thesis explores several applications of anyon condensation as a mechanism to characterize and implement non-invertible symmetries in gauge theories in two and three spacetime dimensions. First, we propose that the concept of level-rank duality can be understood in full generality by considering non-invertible symmetries as gauge symmetries, leading to a broad generalization of examples and a unified understanding of previously known examples. We also study the relation between non-invertible symmetries and the coset construction of 2D CFT. In particular, we describe topological cosets – defined by the case where the coset CFT has a vanishing central charge – and apply the results to find non-invertible symmetries of 2D QCD. In particular, this is used to describe the low-energy regime of 2D QCD and to constrain the energy spectrum of gapped 2D QCD. Finally, we use anyon condensation to argue for the existence of non-invertible one-form symmetry at the transition point of certain Chern-Simons matter RG flows triggered by the Higgs mechanism.