Abstract
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.
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Yagi, J. Ω-deformation and quantization. J. High Energ. Phys. 2014, 112 (2014). https://doi.org/10.1007/JHEP08(2014)112
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DOI: https://doi.org/10.1007/JHEP08(2014)112