A mathematical theory of the gauged linear sigma model

Fan, Huijun¹ ; Jarvis, Tyler² ; Ruan, Yongbin³

¹ School of Mathematical Science, Beijing (Peking) University, Beijing, China
² Department of Mathematics, Brigham Young University, Provo, UT, United States
³ Mathematics Department, University of Michigan, Ann Arbor, MI, United States, Beijing International Center for Mathematical Science, Peking University, Beijing, China

Geometry & topology, Tome 22 (2018) no. 1, pp. 235-303.

Résumé

We construct a mathematical theory of Witten’s Gauged Linear Sigma Model (GLSM). Our theory applies to a wide range of examples, including many cases with nonabelian gauge group.

Both the Gromov–Witten theory of a Calabi–Yau complete intersection $X$ and the Landau–Ginzburg dual (FJRW theory) of $X$ can be expressed as gauged linear sigma models. Furthermore, the Landau–Ginzburg/Calabi–Yau correspondence can be interpreted as a variation of the moment map or a deformation of GIT in the GLSM. This paper focuses primarily on the algebraic theory, while a companion article will treat the analytic theory.

Détail

DOI : 10.2140/gt.2018.22.235

Classification : 14D23, 14L24, 14N35, 53D45, 81T60, 14J32, 14L30, 32G81, 81T40
Keywords: gauged linear sigma model, mirror symmetry, Gromov–Witten, Calabi–Yau, Landau–Ginzburg

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