Ω-deformation and quantization

  • Junya Yagi
Open Access


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.


Supersymmetric gauge theory Integrable Field Theories 


Open Access

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Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.International School for Advanced Studies (SISSA)TriesteItaly
  2. 2.INFN, Sezione di TriesteTriesteItaly

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