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A Mathematical Theory of the Gauged Linear Sigma Model

Algebraic Geometry 2020-12-01 v5 High Energy Physics - Theory Mathematical Physics math.MP Symplectic Geometry

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.

Keywords

Cite

@article{arxiv.1506.02109,
  title  = {A Mathematical Theory of the Gauged Linear Sigma Model},
  author = {Huijun Fan and Tyler Jarvis and Yongbin Ruan},
  journal= {arXiv preprint arXiv:1506.02109},
  year   = {2020}
}

Comments

Corrections to treatment of compact type