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• W2953668105 abstract "This thesis is devoted to the study of gauged linear sigma models (GLSMs) and mirrorsymmetry. The first chapter of this thesis aims to introduce some basics of GLSMs andmirror symmetry. The second chapter contains the author’s contributions to new exactresults for GLSMs obtained by applying supersymmetric localization. The first part of thatchapter concerns supermanifolds. We use supersymmetric localization to show that A-twistedGLSM correlation functions for certain supermanifolds are equivalent to corresponding Atwisted GLSM correlation functions for hypersurfaces. The second part of that chapterdefines associated Cartan theories for non-abelian GLSMs by studying partition functions aswell as elliptic genera. The third part of that chapter focuses on N =(0,2) GLSMs. For thosedeformed from N =(2,2) GLSMs, we consider A/2-twisted theories and formulate the genuszero correlation functions in terms of Jeffrey-Kirwan-Grothendieck residues on Coulombbranches, which generalize the Jeffrey-Kirwan residue prescription relevant for the N =(2,2)locus. We reproduce known results for abelian GLSMs, and can systematically calculatemore examples with new formulas that render the quantum sheaf cohomology relations andother properties manifest. We also include unpublished results for counting deformationparameters. The third chapter is about mirror symmetry. In the first part of the thirdchapter, we propose an extension of the Hori-Vafa mirrror construction [25] from abelian(2,2) GLSMs they considered to non-abelian (2,2) GLSMs with connected gauge groups, apotential solution to an old problem. We formally show that topological correlation functionsof B-twisted mirror LGs match those of A-twisted gauge theories. In this thesis, we study twoexamples, Grassmannians and two-step flag manifolds, verifying in each case that the mirrorcorrectly reproduces details ranging from the number of vacua and correlations functions toquantum cohomology relations. In the last part of the third chapter, we propose an extensionof the Hori-Vafa construction [25] of (2,2) GLSM mirrors to (0,2) theories obtained from (2,2)theories by special tangent bundle deformations. Our ansatz can systematically produce the(0,2) mirrors of toric varieties and the results are consistent with existing examples whichwere produced by laborious guesswork. The last chapter briefly discusses some directionsthat the author would like to pursue in the future." @default.
• W2953668105 created "2019-07-12" @default.
• W2953668105 creator A5056262119 @default.
• W2953668105 date "2019-07-02" @default.
• W2953668105 modified "2023-10-17" @default.
• W2953668105 title "Gauged Linear Sigma Models and Mirror Symmetry" @default.
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