Lectures on generalized symmetries

Bhardwaj, Lakshya; Bottini, Lea E.; Fraser-Taliente, Ludovic; Gladden, Liam; Gould, Dewi S.W.; Platschorre, Arthur; Tillim, Hannah

doi:10.1016/j.physrep.2023.11.002

Lectures on generalized symmetries

Jul 14, 2023

150 pages

Published in:

Phys.Rept. 1051 (2024) 1-87

Published: Nov 29, 2023
and
Published: Feb 6, 2024

e-Print:

2307.07547 [hep-th]

DOI:

10.1016/j.physrep.2023.11.002 (publication)

View in:

ADS Abstract Service

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Abstract: (Elsevier B.V.)

These are a set of lecture notes on generalized global symmetries in quantum field theory. The focus is on invertible symmetries with a few comments regarding non-invertible symmetries. The main topics covered are the basics of higher-form symmetries and their properties including ’t Hooft anomalies, gauging and spontaneous symmetry breaking. We also introduce the useful notion of symmetry topological field theories (SymTFTs). Furthermore, an introduction to higher-group symmetries describing mixings of higher-form symmetries is provided. Some advanced topics covered include the encoding of higher-form symmetries in holography and geometric engineering constructions in string theory. Throughout the text, all concepts are consistently illustrated using gauge theories as examples.

Note:

138 pages, added references

Symmetries
Anomalies
Quantum field theory
String theory
symmetry: topological
symmetry: global
field theory: topological
engineering: geometrical
lectures
holography

References(221)

Figures(0)

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