Dirac pairings, one-form symmetries and Seiberg-Witten geometries

Abstract

The Coulomb phase of a quantum field theory, when present, illuminates the analysis of its line operators and one-form symmetries. For 4d $\mathcal{N}=2$ field theories the low energy physics of this phase is encoded in the special Kähler geometry of the moduli space of Coulomb vacua. We clarify how the information on the allowed line operator charges and one-form symmetries is encoded in the special Kähler structure. We point out the important difference between the lattice of charged states and the homology lattice of the abelian variety fibered over the moduli space, which, when principally polarized, is naturally identified with a choice of the lattice of mutually local line operators. This observation illuminates how the distinct S-duality orbits of global forms of $\mathcal{N}=4$ theories are encoded geometrically.

v3 - with minor corrections

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• Generalized Global Symmetries
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• Maruyoshi-Song Flows and Defect Groups of $D_p^b(G)$ Theories
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Cited by in corpus (10)

• Symmetry TFTs for 3d QFTs from M-theory
• Anomalies of Generalized Symmetries from Solitonic Defects
• Disconnected 0-Form and 2-Group Symmetries
• Reading between the rational sections: Global structures of 4d $\mathcal{N}=2$ KK theories
• On the Protected Spectrum of the Minimal Argyres-Douglas Theory
• Disconnected gauge groups in the infrared
• Generalized symmetry constraints on deformed 4d (S)CFTs
• Coulomb branch surgery: Holonomy saddles, S-folds and discrete symmetry gaugings
• Towards 6D Little String Theory of Particles
• Completely (iso-)split scale-invariant Coulomb branch geometries are isotrivial