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A mathematical theory of the gauged linear sigma model

Huijun Fan, Tyler J Jarvis and Yongbin Ruan

Geometry & Topology 22 (2018) 235–303

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.

gauged linear sigma model, mirror symmetry, Gromov–Witten, Calabi–Yau, Landau–Ginzburg
Mathematical Subject Classification 2010
Primary: 14D23, 14L24, 14N35, 53D45, 81T60
Secondary: 14J32, 14L30, 32G81, 81T40
Received: 2 November 2015
Revised: 23 December 2016
Accepted: 30 January 2017
Published: 31 October 2017
Proposed: Jim Bryan
Seconded: Richard Thomas, Simon Donaldson
Huijun Fan
School of Mathematical Science
Beijing (Peking) University
Tyler J Jarvis
Department of Mathematics
Brigham Young University
Provo, UT
United States
Yongbin Ruan
Mathematics Department
University of Michigan
Ann Arbor, MI
United States
Beijing International Center for Mathematical Science
Peking University