Non-invertible Symmetry in 4-Dimensional Z2 Lattice Gauge Theory
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Beschreibung
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.
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.
Nominated as an outstanding Ph.D. thesis by Osaka University Provides an introduction to non-invertible symmetries Provides a detailed explanation of the Aasen-Mong-Fendley approach, one way to construct topological operators
Autor*in
Masataka Koide
Themen in »Non-invertible Symmetry in 4-Dimensional Z2 Lattice Gauge Theory«
Generalized Symmetry Non-invertible Symmetry Topological Defect Z2 Lattice Gauge Theory Kramers-Wannier Duality Higher Dimensional Theory