A Mathematical Theory of the Gauged Linear Sigma Model

Abstract

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 non-Abelian 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.

Corrections to treatment of compact type

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• A Brief Survey of FJRW Theory
• Mirror Symmetry for Nonabelian Landau-Ginzburg Models
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• A survey of recent developments in GLSMs
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• The Moduli Space in the Gauged Linear Sigma Model
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