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An Introduction to Higher-Form Symmetries

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arxiv 2303.01817 v2 pith:VSC227II submitted 2023-03-03 hep-th cond-mat.str-el

An Introduction to Higher-Form Symmetries

classification hep-th cond-mat.str-el
keywords symmetrieshigher-formtheorieschargeddiscussgaugeintroductionnotes
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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These notes are intended to be a pedagogical introduction to higher-form symmetries, which are symmetries whose charged objects are extended operators supported on lines, surfaces, and etc. This subject has been one of the most popular and effervescent topics of theoretical physics in recent years. Gauge theories are central in the study of higher-form symmetries, with Wilson and 't Hooft operators corresponding to the charged objects. Along these notes, we discuss in detail some basic aspects, including Abelian Maxwell and Chern-Simons theories, and $SU(N)$ non-Abelian gauge theories. We also discuss spontaneous breaking of higher-form symmetries.

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Cited by 28 Pith papers

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