Topics in generalized symmetries in the continuum and on the lattice

Abstract

This dissertation explores topics in quantum field theory from the perspective of generalized symmetries. Driven by new ideas in condensed matter and high energy physics, the notion of symmetry has been significantly expanded in recent years, giving rise to new insights and constraints on strongly-coupled quantum field theories. In this thesis we focus on the implications of higher-form symmetries for confining gauge theories, and discuss lattice discretizations of continuum quantum field theories where such global symmetries can be analyzed in a concrete setting. In the continuum, we examine the interplay between confinement and 1-form symmetries in gauge theories. We point out that in two spacetime dimensions, theories with 1-form symmetries necessarily have relevant deformations which directly impact confinement. We also show that SU(N) QCD with fundamental quarks has no emergent 1-form symmetry in the large N limit, despite the fact that the theory is confining at large N. On the lattice, we employ a recently-discovered approach known as the modified Villain formulation to discretize abelian Chern-Simons theory. We take particular care to maintain its global structure, symmetries, and 't Hooft anomalies at the lattice level. This thesis also contains an introduction to some basic concepts in generalized symmetries along with illustrative examples.