Magnetic Higher-Form Symmetries as Dual Fundamental ∞-Groupoids
Abstract
We develop a higher-geometric framework for magnetic higher-form symmetries of pre-quantum field theories. The magnetic (topological) charges of a sigma-model with stacky target are encoded by the shape of the target, equivalently of its stack of fields, which is op-dual to the flat automorphism group controlling electric symmetries. Magnetic symmetry backgrounds are obtained by dualizing these charges against a chosen moduli stack of topological field theories, generalizing Pontryagin duality, and act on the theory by stacking. Cohesive modalities allow for targets with non-finite and non-discrete data. When the dualizing stack is a grouplike E∞-object, we prove a fibration theorem expressing the magnetic symmetries of an electrically gauged theory in terms of those of the ungauged theory and of the gauge group, computed by a homotopy-fixed-point spectral sequence with an explicit first page. For moduli stacks of higher U(1)-gerbes with connection, encoding bulk topological local Lagrangians, we prove a factorization theorem: the magnetic symmetry backgrounds of any connected target split, non-canonically, into Pontryagin duals of its integral homology groups, and are necessarily flat, as a consequence of dualizing discrete charges against a target with connections. We illustrate both theorems with pure Pin±(2) gauge theory: O(2) carries invertible magnetic ℤ2 symmetries in form degrees d−3, d−4 and d−5 that are absent for Pin-(2), the first two distinguished by a single differential of the spectral sequence. Gauging and physical applications are developed in upcoming work.
Related
- Symmetries and Higher-Form Connections in Derived Differential Geometry
- S-duality, boundary states, and higher-form symmetries on ALE spaces
- The shifted symplectic geometry of derived higher groupoids
- Higher Groupoids of Gauge Potentials in Higher Gauge Theories admitting Weights
- Magnetic cotangent groupoids
BibTeX
@misc{perezlona2026magnetic,
title = {{Magnetic Higher-Form Symmetries as Dual Fundamental $\infty$-Groupoids}},
author = {Alonso Perez-Lona},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03865},
eprint = {2610.03865},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03865},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Magnetic Higher-Form Symmetries as Dual Fundamental ∞-Groupoids
AU - Alonso Perez-Lona
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03865
UR - https://arxiv.org/abs/2610.03865
AB - We develop a higher-geometric framework for magnetic higher-form symmetries of pre-quantum field theories. The magnetic (topological) charges of a sigma-model with stacky target are encoded by the shape of the target, equivalently of its stack of fields, which is op-dual to the flat automorphism group controlling electric symmetries. Magnetic symmetry backgrounds are obtained by dualizing these charges against a chosen moduli stack of topological field theories, generalizing Pontryagin duality, and act on the theory by stacking. Cohesive modalities allow for targets with non-finite and non-discrete data. When the dualizing stack is a grouplike E_∞-object, we prove a fibration theorem expressing the magnetic symmetries of an electrically gauged theory in terms of those of the ungauged theory and of the gauge group, computed by a homotopy-fixed-point spectral sequence with an explicit first page. For moduli stacks of higher U(1)-gerbes with connection, encoding bulk topological local Lagrangians, we prove a factorization theorem: the magnetic symmetry backgrounds of any connected target split, non-canonically, into Pontryagin duals of its integral homology groups, and are necessarily flat, as a consequence of dualizing discrete charges against a target with connections. We illustrate both theorems with pure Pin^±(2) gauge theory: O(2) carries invertible magnetic ℤ_2 symmetries in form degrees d−3, d−4 and d−5 that are absent for Pin^-(2), the first two distinguished by a single differential of the spectral sequence. Gauging and physical applications are developed in upcoming work.
ER -