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.

arXiv commentv3 - with minor corrections

References in corpus (34)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Generalized Global Symmetries
• N=2 dualities
• Solutions Of Four-Dimensional Field Theories Via M Theory
• Supersymmetric Yang-Mills Systems And Integrable Systems
• Coupling a QFT to a TQFT and Duality
• Reading between the lines of four-dimensional gauge theories
• Wilson-'t Hooft operators in four-dimensional gauge theories and S-duality
• Special Kahler Manifolds
• Notes on Theories with 16 Supercharges
• On the Defect Group of a 6D SCFT
• N=3 four dimensional field theories
• S-folds and 4d N=3 superconformal field theories
• Coulomb and Higgs Branches from Canonical Singularities: Part 0
• Calogero-Moser Systems in SU(N) Seiberg-Witten Theory
• 5d and 4d SCFTs: Canonical Singularities, Trinions and S-Dualities
• Higher Form Symmetries and M-theory
• On the 6d origin of discrete additional data of 4d gauge theories
• N=2 supersymmetric dynamics for pedestrians
• Coulomb and Higgs Branches from Canonical Singularities, Part 1: Hypersurfaces with Smooth Calabi-Yau Resolutions
• VOAs labelled by complex reflection groups and 4d SCFTs
• Higher Form Symmetries of Argyres-Douglas Theories
• Geometric classification of 4d $\mathcal{N}=2$ SCFTs
• Maruyoshi-Song Flows and Defect Groups of $D_p^b(G)$ Theories
• On S-duality for Non-Simply-Laced Gauge Groups
• Spectral Curves for Super-Yang-Mills with Adjoint Hypermultiplet for General Lie Algebras
• 1-Form Symmetry, Isolated N=2 SCFTs, and Calabi-Yau Threefolds
• Exceptional $\mathcal{N}=3$ theories
• Line Operators of Gauge Theories on Non-Spin Manifolds
• Dynamical consequences of 1-form symmetries and the exceptional Argyres-Douglas theories
• Testing our understanding of SCFTs: a catalogue of rank-2 $\mathcal{N}$=2 theories in four dimensions
• Classification of all $\mathcal{N}\ge 3$ moduli space orbifold geometries at rank 2
• Exceptional moduli spaces for exceptional $\mathcal{N}=3$ theories

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