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

Abstract

We study two-dimensional $\mathcal{N}=(0,2)$ supersymmetric gauged linear sigma models (GLSMs) using supersymmetric localization. We consider $\mathcal{N}=(0,2)$ 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 $\mathcal{N}=(2,2)$ 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 $\mathcal{N}=(2,2)$ 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 $\mathcal{N}=(2,2)$ 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.

39 pages plus appendices. v2: added references and corrected typos

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• Comments on N=(2,2) Supersymmetry on Two-Manifolds
• The Revival of (0,2) Linear Sigma Models
• A-twisted heterotic Landau-Ginzburg models
• Half-Twisted (0,2) Landau-Ginzburg Models
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Cited by in corpus (24)

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• Quantum sheaf cohomology on Grassmannians
• A-twisted correlators and Hori dualities
• The Green-Schwarz Mechanism and Geometric Anomaly Relations in 2d (0,2) F-theory Vacua
• M5-branes on S^2 x M_4: Nahm's Equations and 4d Topological Sigma-models
• A proposal for (0,2) mirrors of toric varieties
• $\mathcal{G}$-structure symmetries and anomalies in $(1,0)$ non-linear $\sigma$-models
• More Toda-like (0,2) mirrors
• Recent developments in 2d $\mathcal{N}=(2,2)$ supersymmetric gauge theories
• Supersymmetric gauged matrix models from dimensional reduction on a sphere
• (0,2) hybrid models
• Quantum Sheaf Cohomology and Duality of Flag Manifolds
• Quantized Coulomb Branches, Monopole Bubbling and Wall-Crossing Phenomena in 3d $\mathcal{N}=4$ Theories
• (0,2) versions of exotic (2,2) GLSMs
• Toda-like (0,2) mirrors to products of projective spaces
• New Evidence for (0,2) Target Space Duality
• Correlation functions in massive Landau-Ginzburg orbifolds and tests of dualities
• Testing the (0,2) mirror map
• Fixed points of (0,2) Landau-Ginzburg renormalization group flows and the chiral algebra
• Quantum cohomology of symplectic flag manifolds
• Supersymmetric Localization in GLSMs for Supermanifolds