Non-invertible Symmetry in 4-Dimensional Z2 Lattice Gauge Theory

This book provides a method for concretely constructing defects that represent non-invertible symmetries in four-dimensional lattice gauge theory. In terms of generalized symmetry, a symmetry is considered to be equivalent to a topological operator whose value does not change even if the shape is topologically transformed. Even for models that lack symmetry in the traditional sense and are difficult to analyze, it is possible to analyze them as long as a generalized symmetry exists. Therefore, generalized symmetry is important for the non-perturbative analysis of quantum field theory. Some topological operators have no group structure, and the corresponding symmetries are called non-invertible symmetries. Concrete examples of non-invertible symmetries in higher-dimensional theories were discovered around 2020, and they have been actively studied as a field of generalized symmetries since then. This book explains the non-invertible symmetry represented by the Kramers-Wannier-Wegner duality, which was found firstly in a four-dimensional theory, represented by three-dimensional defects. This book is intended for those with preliminary knowledge of quantum field theory and statistical mechanics.