2014/05/31 by Junya Yagi
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Canonical quantization #Geometric quantization #Holomorphic function #Homotopy and Cohomology in Algebraic Topology #Integrable system #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Omega #Physics #Pure mathematics #Quantization (signal processing) #Quantum #Quantum gravity #Quantum mechanics #Riemann surface #Submanifold #Symplectic geometry #Symplectic manifold #hep-th
paper · pdf · doi:10.1007/jhep08(2014)112
published as JHEP08(2014)112 · 24 pages. v2: minor changes, references added; v3: minor changes, a reference added, published version
openalex publication_date 2014/08/01 · arxiv created 2014/08/30 · arxiv updated 2014/09/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We formulate a deformation of Rozansky-Witten theory analogous to the Ω-deformation. It is applicable when the target space X is hyperkähler and the spacetime is of the form ℝ×Σ, with Σ being a Riemann surface. In the case that Σ is a disk, the Ω-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 Ω-deformation and quantization of integrable systems. The other concerns supersymmetric loop operators and quantization of the algebra of holomorphic functions on a hyperkähler manifold.