Non-invertible Symmetry in 4-Dimensional Z2 Lattice Gauge Theory / by Masataka Koide.

Format:

Book

Author/Creator:

Koide, Masataka., Author.

Series:

Springer Theses, Recognizing Outstanding Ph.D. Research, 2190-5061

Language:

English

Subjects (All):

Particles (Nuclear physics).

Quantum field theory.

Mathematical physics.

Elementary Particles, Quantum Field Theory.

Mathematical Physics.

Mathematical Methods in Physics.

Local Subjects:

Elementary Particles, Quantum Field Theory.

Mathematical Physics.

Mathematical Methods in Physics.

Physical Description:

1 online resource (XIV, 88 p. 89 illus., 74 illus. in color.)

Edition:

1st ed. 2025.

Place of Publication:

Singapore : Springer Nature Singapore : Imprint: Springer, 2025.

Summary:

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.

Contents:

Chapter 1 Introduction

Chapter 2 Symmetry and Topological defect

Chapter 3 Ising model and Kramers-Wannier duality

Chapter 4 KWW defect in 4-dimensional lattice gauge theory

Chapter 5 Application to g-functions

Chapter 6 Conclusion and discussion

Appendix.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9789819622726

9819622727

OCLC:

1515507232