UCLA

This dissertation is a collection of work on several aspects of quantum field theory, including the worldsheet dynamics of vortex strings, non-invertible symmetries and their holographic realizations, and quantum field theory in non-integer spacetime dimensions.In Chapter 2, we study string excitations and the effective worldsheet action of Abrikosov–Nielsen–Olesen vortex strings in the four-dimensional Abelian Higgs model. We analyze fluctuations around the vortex and determine the worldsheet spectrum. Interestingly, we find a light dilaton in the type-I regime and a light axion in the type-II regime. By integrating out the massive modes, we compute the O(K4 ) Wilson coefficients of the effective string action and compare the resulting theory with flux-tube S-matrix bootstrap constraints and Yang–Mills confining strings. We also discuss the implications of this comparison for the dual superconductor picture of confinement.In Chapter 3, we study non-invertible defects in two-dimensional SN orbifold CFTs. We construct universal defects which do not depend on the details of the seed CFT and hence exist in any orbifold CFT. Additionally, we investigate non-universal defects arising from the topological defects of the seed CFT. We argue that there exist universal defects that are non-trivial in the large-N limit, making them relevant for the AdS3/CFT2 correspondence. We then focus on AdS3 × S 3 × M4 with one unit of NS–NS flux and propose an explicit realization of these defects on the worldsheet. We also calculate the entanglement entropy in symmetric orbifold CFTs in the presence of topological defects.In Chapter 4, we revisit the old problem of analytically continuing quantum field theories to fractional dimension d ∈ C. We observe that common theories such as QCD and QED have branch cuts in the complex d plane. In particular, many operators in their low-energy CFTs have OPEs and scaling dimensions that jump as a function of d.