Coulomb Branch Quantization and Abelianized Monopole Bubbling

Abstract

We develop an approach to the study of Coulomb branch operators in 3D $\mathcal{N}=4$ gauge theories and the associated quantization structure of their Coulomb branches. This structure is encoded in a one-dimensional TQFT subsector of the full 3D theory, which we describe by combining several techniques and ideas. The answer takes the form of an associative and noncommutative star product algebra on the Coulomb branch. For `good' and `ugly' theories (according to the Gaiotto-Witten classification), we also exhibit a trace map on this algebra, which allows for the computation of correlation functions and, in particular, guarantees that the star product satisfies a truncation condition. This work extends previous work on abelian theories to the non-abelian case by quantifying the monopole bubbling that describes screening of GNO boundary conditions. In our approach, monopole bubbling is determined from the algebraic consistency of the OPE. This also yields a physical proof of the Bullimore-Dimofte-Gaiotto abelianization description of the Coulomb branch.

73 pages plus appendices; v2: improved presentation, updated references and acknowledgements, added comments and appendices; v3: fixed a reference, matches published version

References in corpus (13)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Fractional M2-branes
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Notes on SUSY Gauge Theories on Three-Sphere
• Level/rank Duality and Chern-Simons-Matter Theories
• Cardy Formulae for SUSY Theories in d=4 and d=6
• Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups
• Supersymmetry enhancement by monopole operators
• Nonsupersymmetric dualities from mirror symmetry
• More Abelian Dualities in 2+1 Dimensions
• Ω-deformation and quantization
• Monopoles in CP(N-1) model via the state-operator correspondence
• Non-Abelian 3d Bosonization and Quantum Hall States

Cited by in corpus (30)

• $\mathcal{N}=4$ Super-Yang-Mills Correlators at Strong Coupling from String Theory and Localization
• AdS${}_4$/CFT${}_3$ from Weak to Strong String Coupling
• The M-theory Archipelago
• Mirror symmetry and line operators
• Taming Defects in $\mathcal{N}=4$ Super-Yang-Mills
• Boundaries, Vermas, and Factorisation
• Folding Orthosymplectic Quivers
• Fibrations and Hasse diagrams for 6d SCFTs
• Balanced B and D-type orthosymplectic quivers -- Magnetic quivers for product theories
• Quiver origami: discrete gauging and folding
• Sphere correlation functions and Verma modules
• Three Dimensional Mirror Symmetry beyond $ADE$ quivers and Argyres-Douglas theories
• The 3d $\mathcal{N}=6$ Bootstrap: From Higher Spins to Strings to Membranes
• More on holographic correlators: Twisted and dimensionally reduced structures
• Topological Correlators and Surface Defects from Equivariant Cohomology
• One-Dimensional Sectors From the Squashed Three-Sphere
• 3d N=4 Bootstrap and Mirror Symmetry
• Localization and Duality for ABJM Latitude Wilson Loops
• Correlators on the wall and ${\mathfrak{sl}}_n$ spin chain
• Deformation quantizations from vertex operator algebras
• Nonabelian Mirror Symmetry Beyond the Chiral Ring
• On Supersymmetric Interface Defects, Brane Parallel Transport, Order-Disorder Transition and Homological Mirror Symmetry
• Quantized Coulomb Branches, Monopole Bubbling and Wall-Crossing Phenomena in 3d $\mathcal{N}=4$ Theories
• Algebras, traces, and boundary correlators in $\mathcal{N}=4$ SYM
• Crystal bases and three-dimensional $\mathcal{N}=4$ Coulomb branches
• Line Operators in 4d Chern-Simons Theory and Cherkis Bows
• Three-Point Functions in ABJM and Bethe Ansatz
• The Holographic Contributions to the Sphere Free Energy
• Fermi-gas correlators of ADHM theory and triality symmetry
• Generating functions for Higgs/Coulomb branch operators from 1d-3d cohomological equivalence