Abstract
We study two-dimensional \( \mathcal{N}=\left(0,\ 2\right) \) supersymmetric gauged linear sigma models (GLSMs) using supersymmetric localization. We consider \( \mathcal{N}=\left(0,\ 2\right) \) 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 \( \mathcal{N}=\left(2,\ 2\right) \) 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 \( \mathcal{N}=\left(2,\ 2\right) \) 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 \( \mathcal{N}=\left(2,\ 2\right) \) 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.
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Closset, C., Gu, W., Jia, B. et al. Localization of twisted \( \mathcal{N}=\left(0,\;2\right) \) gauged linear sigma models in two dimensions. J. High Energ. Phys. 2016, 70 (2016). https://doi.org/10.1007/JHEP03(2016)070
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DOI: https://doi.org/10.1007/JHEP03(2016)070