Chiral trace relations in $\Omega$-deformed $\mathcal N=2$ theories

Understand

We consider $\mathcal N=2$ $SU(2)$ gauge theories in four dimensions (pure or mass deformed) and discuss the properties of the simplest chiral observables in the presence of a generic $\Omega$-deformation.

• We compute them by equivariant localization and analyze the structure of the exact instanton corrections to the classical chiral ring relations.
• We predict exact relations valid at all instanton number among the traces $\langle\text{Tr}\varphi^{n}\rangle$, where $\varphi$ is the scalar field in the gauge multiplet.
• In the Nekrasov-Shatashvili limit, such relations may be explained in terms of the available quantized Seiberg-Witten curves.