Localization of twisted N = 0 , 2 $$ mathcal{N}=left(0,;2right) $$ gauged linear sigma models in two dimensions

We study two-dimensional $$ mathcal{n}=left(0, 2right) $$ supersymmetric gauged linear sigma models (glsms) using supersymmetric localization. we consider $$ mathcal{n}=left(0, 2right) $$ theories with an r-symmetry, which can always be defined on curved space by a pseudo-topological twist while preserving one of the two supercharges of flat space. for glsms which are deformations of $$ mathcal{n}=left(2, 2right) $$ glsms and retain a coulomb branch, we consider the a/2-twist and compute the genus-zero correlation functions of certain pseudo-chiral operators, which generalize the simplest twisted chiral ring operators away from the $$ mathcal{n}=left(2, 2right) $$ locus. these correlation functions can be written in terms of a certain residue operation on the coulomb branch, generalizing the jeffrey-kirwan residue prescription relevant for the $$ mathcal{n}=left(2, 2right) $$ locus. for abelian glsms, we reproduce existing results with new formulas that render the quantum sheaf cohomology relations and other properties manifest. for non-abelian glsms, our methods lead to new results. as an example, we briefly discuss the quantum sheaf cohomology of the grassmannian manifold.