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arXiv · 1504.06308

The equivariant A-twist and gauged linear sigma models on the two-sphere

Cyril Closset·Stefano Cremonesi·Daniel S. Park
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Abstract

We study two-dimensional $\mathcal{N}=(2,2)$ supersymmetric gauged linear sigma models (GLSM) on the $Ω$-deformed sphere, $S^2_Ω$, which is a one-parameter deformation of the $A$-twisted sphere. We provide an exact formula for the $S^2_Ω$ 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 present a complementary Higgs branch localization scheme in the special case of abelian gauge groups.

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Cyril Closset, Stefano Cremonesi, Daniel S. Park. 2015-09-22. The equivariant A-twist and gauged linear sigma models on the two-sphere. https://doi.org/10.1007/jhep06(2015)076

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