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We investigate an alternative approach to the correspondence offour-dimensional $\mathcal{N}=2$ superconformal theories and two-dimensionalvertex operator algebras, in the framework of the $\Omega$-deformation ofsupersymmetric gauge theories. The two-dimensional $\Omega$-deformation of theholomorphic-topological theory on the product four-manifold is constructed atthe level of supersymmetry variations and the action. The supersymmetriclocalization is performed to achieve a two-dimensional chiral CFT. The desiredvertex operator algebra is recovered as the algebra of local operators of theresulting CFT. We also discuss the identification of the Schur index of the$\mathcal{N}=2$ superconformal theory and the vacuum character of the vertexoperator algebra at the level of their path integral representations, using our$\Omega$-deformation point of view on the correspondence.

SCFT/VOA correspondence via $\Omega$-deformation