Higher-Form Symmetry in a Nutshell

yzj5306@psu.edu (Yiyang Jiang) — Mon, 31 Aug 2026 17:00:00 -0400


Presenter	Jinfei Zhou (Prof. Zhen Bi’s group, Penn State)
Date	August 31, 2026 · 5:00–6:00 PM — continued September 7, 2026 · 4:30–6:00 PM
Location	Davey 339
Topic	Higher-form symmetry — from differential forms to the generalized Landau paradigm

Landau’s paradigm says a phase is labelled by a symmetry and how it breaks, and that the critical modes are order-parameter fluctuations. Three familiar things appear to escape it: topological order, confinement/deconfinement, and the exact masslessness of the photon — none of them has a local order parameter. The claim of this talk is that all three are symmetry-breaking phenomena, once you allow the symmetry to act on loops and surfaces rather than on points. The route there is a single conceptual pivot: a symmetry is not a transformation of the fields but a topological operator supported on a submanifold, and the only thing being generalized is the dimension of that support. Two sessions took the argument from differential forms and linking numbers, through the recasting of ordinary Noether symmetry as a codimension-1 defect, to the definition of $p$-form symmetry and its realizations in Maxwell theory, the toric code, $\mathbb{Z}_N$ gauge theory, Chern–Simons theory and the $\mathbb{Z}_N$ center of Yang–Mills — ending with generalized order parameters, the photon as a Goldstone boson, a higher-form Mermin–Wagner theorem, and ’t Hooft anomalies.

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Higher-Form Symmetry in a Nutshell