TY - JOUR
T1 - Analysis of gauged Witten equation
AU - Tian, Gang
AU - Xu, Guangbo
N1 - Funding Information:
This work was supported in part by the National Key Research and Development Program of China (Grant No. 2016YFD0101002), the Agricultural Science and Technology Innovation Program of CAAS, the USDA?s National Institute of Food and Agriculture (award No. 2018-67013-28511), and the US National Science Foundation (awards No. 1741090). We are grateful for the support from the Kansas Agricultural Experiment Station (contribution No.19-310-J).
Funding Information:
2018-67013-28511), and the US National Science Foundation (awards No. 1741090). We are grateful for the support from the Kansas Agricultural Experiment Station (contribution No.19-310-J).
Funding Information:
This work was supported in part by the National Key Research and Development Program of China (Grant No. 2016YFD0101002), the Agricultural Science and Technology Innovation Program of CAAS, the USDA’s National Institute of Food and Agriculture (award No.
Publisher Copyright:
© 2015 De Gruyter.
PY - 2015
Y1 - 2015
N2 - The gauged Witten equation was essentially introduced by Witten in his formulation of the gauged linear σ-model (GLSM), which explains the so-called Landau-Ginzburg/Calabi-Yau correspondence. This is the first paper in a series towards a mathematical construction of GLSM, in which we set up a proper framework for studying the gauged Witten equation and its perturbations. We also prove several analytical properties of solutions and moduli spaces of the perturbed gauged Witten equation. We prove that solutions have nice asymptotic behavior on cylindrical ends of the domain. Under a good perturbation scheme, the energies of solutions are shown to be uniformly bounded by a constant depending only on the topological type. We prove that the linearization of the perturbed gauged Witten equation is Fredholm, and we calculate its Fredholm index. Finally, we define a notion of stable solutions and prove a compactness theorem for the moduli space of solutions over a fixed domain curve.
AB - The gauged Witten equation was essentially introduced by Witten in his formulation of the gauged linear σ-model (GLSM), which explains the so-called Landau-Ginzburg/Calabi-Yau correspondence. This is the first paper in a series towards a mathematical construction of GLSM, in which we set up a proper framework for studying the gauged Witten equation and its perturbations. We also prove several analytical properties of solutions and moduli spaces of the perturbed gauged Witten equation. We prove that solutions have nice asymptotic behavior on cylindrical ends of the domain. Under a good perturbation scheme, the energies of solutions are shown to be uniformly bounded by a constant depending only on the topological type. We prove that the linearization of the perturbed gauged Witten equation is Fredholm, and we calculate its Fredholm index. Finally, we define a notion of stable solutions and prove a compactness theorem for the moduli space of solutions over a fixed domain curve.
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U2 - 10.1515/crelle-2015-0066
DO - 10.1515/crelle-2015-0066
M3 - Article
AN - SCOPUS:84962944520
VL - 2015
SP - 187
EP - 274
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
SN - 0075-4102
ER -