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

  • Cyril Closset
  • Wei Gu
  • Bei Jia
  • Eric Sharpe
Open Access
Regular Article - Theoretical Physics

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.

Keywords

Field Theories in Lower Dimensions Supersymmetric gauge theory Topological Field Theories 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Simons Center for Geometry and PhysicsState University of New YorkStony BrookU.S.A.
  2. 2.Department of Physics MC 0435Virginia TechBlacksburgU.S.A.
  3. 3.Theory Group, Physics DepartmentUniversity of TexasAustinU.S.A.

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