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

Closset, Cyril and Cremonesi, Stefano and Park, Daniel S. (2015) 'The equivariant A-twist and gauged linear sigma models on the two-sphere.', Journal of high energy physics., 2015 (06). 076.


We study two-dimensional N=(2,2)N=(2,2) supersymmetric gauged linear sigma models (GLSM) on the Ω-deformed sphere, SΩ2, which is a one-parameter deformation of the A-twisted sphere. We provide an exact formula for the SΩ2 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 ϵΩ-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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Publisher statement:Open Access, © The Author(s) 2015. Article funded by SCOAP3. 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.
Date accepted:19 May 2015
Date deposited:29 March 2017
Date of first online publication:12 June 2015
Date first made open access:No date available

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