Nonabelian gauged linear sigma model (English)

In: Chinese Annals of Mathematics, Series B   ;  38 ,  4  ;  963-984  ;  2017

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The gauged linear sigma model (GLSM for short) is a 2d quantum field theory introduced by Witten twenty years ago. Since then, it has been investigated extensively in physics by Hori and others. Recently, an algebro-geometric theory (for both abelian and nonabelian GLSMs) was developed by the author and his collaborators so that he can start to rigorously compute its invariants and check against physical predications. The abelian GLSM was relatively better understood and is the focus of current mathematical investigation. In this article, the author would like to look over the horizon and consider the nonabelian GLSM. The nonabelian case possesses some new features unavailable to the abelian GLSM. To aid the future mathematical development, the author surveys some of the key problems inspired by physics in the nonabelian GLSM.

Table of contents – Volume 38, Issue 4

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A survey on mixed spin P-fields
Chang, Huai-Liang / Li, Jun / Li, Wei-Ping / Liu, Chiu-Chu Melissa | 2017
Landau-Ginzburg/Calabi-Yau correspondence via wall-crossing
Choi, Jinwon / Kiem, Young-Hoon | 2017
Beijing lectures on the grade restriction rule
Eager, Richard / Hori, Kentaro / Knapp, Johanna / Romo, Mauricio | 2017
The moduli space in the gauged linear sigma model
Fan, Huijun / Jarvis, Tyler / Ruan, Yongbin | 2017
Cluster partition function and invariants of 3-manifolds
Romo, Mauricio | 2017
Nonabelian gauged linear sigma model
Ruan, Yongbin | 2017
Geometry of the second-order tangent bundles of Riemannian manifolds
Gezer, Aydin / Magden, Abdullah | 2017
On Hopf Galois extension of separable algebras
Lu, Yu / Zhu, Shenglin | 2017
L-factor of irreducible χ1 × χ2 ⋊ σ
Danisman, Yusuf | 2017