Ω-deformation and quantization

Abstract

We formulate a deformation of Rozansky-Witten theory analogous to the $\Omega$-deformation. It is applicable when the target space $X$ is hyperkähler and the spacetime is of the form $\mathbb{R}\times \Sigma$, with $\Sigma$ being a Riemann surface. In the case that $\Sigma$ is a disk, the $\Omega$-deformed Rozansky-Witten theory quantizes a symplectic submanifold of $X$, thereby providing a new perspective on quantization. As applications, we elucidate two phenomena in four-dimensional gauge theory from this point of view. One is a correspondence between the $\Omega$-deformation and quantization of integrable systems. The other concerns supersymmetric loop operators and quantization of the algebra of holomorphic functions on a hyperkähler manifold.

24 pages. v2: minor changes, references added; v3: minor changes, a reference added, published version

References in corpus (24)

• N=2 dualities
• Supersymmetric Yang-Mills Systems And Integrable Systems
• Four-dimensional wall-crossing via three-dimensional field theory
• Janus Configurations, Chern-Simons Couplings, And The Theta-Angle in N=4 Super Yang-Mills Theory
• Vortex Counting and Lagrangian 3-manifolds
• The Omega Deformation, Branes, Integrability, and Liouville Theory
• Remarks on A-branes, Mirror Symmetry, and the Fukaya category
• Quantum Geometry of Refined Topological Strings
• SL(2,R) Chern-Simons, Liouville, and Gauge Theory on Duality Walls
• Exact Kahler Potential from Gauge Theory and Mirror Symmetry
• Gauge theories on Omega-backgrounds from non commutative Seiberg-Witten curves
• Exact Results In Two-Dimensional (2,2) Supersymmetric Gauge Theories With Boundary
• Topological Matter in Two Dimensions
• 3d Chern-Simons Theory from M5-branes
• Branes and Quantization
• Comments on N=(2,2) Supersymmetry on Two-Manifolds
• Line operators on S^1xR^3 and quantization of the Hitchin moduli space
• 3-Manifolds and 3d Indices
• 3d TQFT from 6d SCFT
• On F-term contribution to effective action
• Chern-Simons-Rozansky-Witten topological field theory
• Twisted N=2 Supersymmetry with Central Charge and Equivariant Cohomology
• N=2 Supersymmetric QCD and Four Manifolds; (I) the Donaldson and the Seiberg-Witten Invariants
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Cited by in corpus (36)

• Boundaries, Mirror Symmetry, and Symplectic Duality in 3d $\mathcal{N}=4$ Gauge Theory
• Deformation quantization and superconformal symmetry in three dimensions
• Coulomb Branch Operators and Mirror Symmetry in Three Dimensions
• Webs of W-algebras
• The Coulomb Branch of 3d $\mathcal{N}=4$ Theories
• Mirror symmetry and line operators
• M-theory in the Omega-background and 5-dimensional non-commutative gauge theory
• SCFT/VOA correspondence via $\Omega$-deformation
• Coulomb Branch Quantization and Abelianized Monopole Bubbling
• Chiral algebras from Ω-deformation
• Boundaries, Vermas, and Factorisation
• Twisted M2 brane holography and sphere correlation functions
• Topological Holography: The Example of The D2-D4 Brane System
• Sphere correlation functions and Verma modules
• Feynman diagrams and $\Omega$-deformed M-theory
• Ω-deformation of B-twisted gauge theories and the 3d-3d correspondence
• Equivariant Verlinde formula from fivebranes and vortices
• Superspin chains from superstring theory
• Poisson vertex algebras in supersymmetric field theories
• Wilson-'t Hooft lines as transfer matrices
• Twisted holography of defect fusions
• Coulomb Branches of Star-Shaped Quivers
• Integrable 3D lattice model in M-theory
• Nonabelian Mirror Symmetry Beyond the Chiral Ring
• 4d/2d $\to$ 3d/1d: A song of protected operator algebras
• Wall-crossing and operator ordering for 't Hooft operators in N=2 gauge theories
• Evidence for an Algebra of ${\mathbf{G}}_2$ Instantons
• Masses, Sheets and Rigid SCFTs
• Branes and DAHA Representations
• Algebras, traces, and boundary correlators in $\mathcal{N}=4$ SYM
• Disk, interval, point: on constructions of quantum field theories with holomorphic action functionals
• Secondary products in supersymmetric field theory
• Line Operators in 4d Chern-Simons Theory and Cherkis Bows
• Fermi-gas correlators of ADHM theory and triality symmetry
• SUSY localization for Coulomb branch operators in omega-deformed 3d N=4 gauge theories
• The quantum UV-IR map for line defects in $\mathfrak{gl}(3)$-type class $S$ theories