This is a survey article for the mathematical theory of Witten's Gauged Linear Sigma Model, as developed recently by the authors. Instead of developing the theory in the most general setting, in this paper the aut...This is a survey article for the mathematical theory of Witten's Gauged Linear Sigma Model, as developed recently by the authors. Instead of developing the theory in the most general setting, in this paper the authors focus on the description of the moduli.展开更多
The authors describe the relationships between categories of B-branes in dif- ferent phases of the non-Abelian gauged linear sigma model. The relationship is described explicitly for the model proposed by Hori and Ton...The authors describe the relationships between categories of B-branes in dif- ferent phases of the non-Abelian gauged linear sigma model. The relationship is described explicitly for the model proposed by Hori and Tong with non-Abelian gauge group that connects two non-birational Calabi-Yau varieties studied by Rcdland. A grade restriction rule for this model is derived using the hemisphere partition function and it is used to map B-type D-branes between the two Calabi-Yau varieties.展开更多
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...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 ahelian GLSM. To aid the future mathematical development, the author surveys some of the key problems inspired by physics in the nonabelian GLSM.展开更多
This is the second paper in a series following Tian and Xu(2015), on the construction of a mathematical theory of the gauged linear σ-model(GLSM). In this paper, assuming the existence of virtual moduli cycles and th...This is the second paper in a series following Tian and Xu(2015), on the construction of a mathematical theory of the gauged linear σ-model(GLSM). In this paper, assuming the existence of virtual moduli cycles and their certain properties, we define the correlation function of GLSM for a fixed smooth rigidified r-spin curve.展开更多
基金supported by the Natural Science Foundation(Nos.DMS-1564502,DMS-1405245,DMS-1564457)the National Natural Science Foundation of China(Nos.11325101,11271028)the Ph.D.Programs Foundation of Ministry of Education of China(No.20120001110060)
文摘This is a survey article for the mathematical theory of Witten's Gauged Linear Sigma Model, as developed recently by the authors. Instead of developing the theory in the most general setting, in this paper the authors focus on the description of the moduli.
文摘The authors describe the relationships between categories of B-branes in dif- ferent phases of the non-Abelian gauged linear sigma model. The relationship is described explicitly for the model proposed by Hori and Tong with non-Abelian gauge group that connects two non-birational Calabi-Yau varieties studied by Rcdland. A grade restriction rule for this model is derived using the hemisphere partition function and it is used to map B-type D-branes between the two Calabi-Yau varieties.
基金supported by the Natural Science Foundation(Nos.DMS 1159265,DMS 1405245)
文摘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 ahelian GLSM. To aid the future mathematical development, the author surveys some of the key problems inspired by physics in the nonabelian GLSM.
基金supported by National Science Foundation of USA(Grant No.DMS-1309359)National Natural Science Foundation of China(Grant No.11331001)
文摘This is the second paper in a series following Tian and Xu(2015), on the construction of a mathematical theory of the gauged linear σ-model(GLSM). In this paper, assuming the existence of virtual moduli cycles and their certain properties, we define the correlation function of GLSM for a fixed smooth rigidified r-spin curve.
