\Omega-deformation and quantization

Understand

We formulate a deformation of Rozansky-Witten theory analogous to the $\Omega$-deformation.

• It is applicable when the target space $X$ is hyperk\"ahler 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.