The equivariant A-twist and gauged linear sigma models on the two-sphere
- Closset, CyrilSimons Center for Geometry and Physics, State University of New York, Stony Brook, NY, 11794, U.S.A.
- Cremonesi, Stefano(Department of Mathematics, King’s College London, The Strand, London, WC2R 2LS, U.K.)
- Park, Daniel(Simons Center for Geometry and Physics, State University of New York, Stony Brook, NY, 11794, U.S.A.)
DOIAbstract
We study two-dimensional N = 2 , 2 $$ \mathcal{N}=\left(2,\;2\right) $$ supersymmetric gauged linear sigma models (GLSM) on the Ω-deformed sphere, S Ω 2 , which is a one-parameter deformation of the A -twisted sphere. We provide an exact formula for the S Ω 2 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 Ω-deformation, the localization formula greatly simplifies the computation of A -twisted correlation functions, and leads to new results for non-abelian theories. We discuss a number of examples and comment on the ϵ Ω -deformation of the quantum cohomology relations. Finally, we p...
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