Higher-form symmetries and spontaneous symmetry breaking

Abstract

We study various aspects of spontaneous symmetry breaking in theories that possess higher-form symmetries, which are symmetries whose charged objects have a dimension $p>0$. We first sketch a proof of a higher version of Goldstone's theorem, and then discuss how boundary conditions and gauge-fixing issues are dealt with in theories with spontaneously broken higher symmetries, focusing in particular on $p$-form $U(1)$ gauge theories. We then elaborate on a generalization of the Coleman-Mermin-Wagner theorem for higher-form symmetries, namely that in spacetime dimension $D$, continuous $p$-form symmetries can never be spontaneously broken if $p\ge D-2$. We also make a few comments on relations between higher symmetries and asymptotic symmetries in Abelian gauge theory.

arXiv comment37 pages

References in corpus (3)

• Generalised global symmetries in states with dynamical defects: the case of the transverse sound in field theory and holography
• Asymptotic Symmetries in $p$-Form Theories
• Gapless Topological Order, Gravity, and Black Holes

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