The equivariant A-twist and gauged linear sigma models on the two-sphere

Understand

We study two-dimensional $\mathcal{N}=(2,2)$ supersymmetric gauged linear sigma models (GLSM) on the $\Omega$-deformed sphere, $S^2_\Omega$, which is a one-parameter deformation of the $A$-twisted sphere.

• We provide an exact formula for the $S^2_\Omega$ supersymmetric correlation functions using supersymmetric localization.
• The contribution of each instanton sector is given in terms of a Jeffrey-Kirwan residue on the Coulomb branch.
• In the limit of vanishing $\Omega$-deformation, the localization formula greatly simplifies the computation of $A$-twisted correlation functions, and leads to new results for non-abelian theories.