A Landau-Ginzburg/Calabi-Yau Correspondence for the Mirror Quintic.

Landau-Ginzburg/Calabi-Yau Correspondence;Mirror Symmetry;Mathematics;Science;Mathematics

Priddis, Nathan CharlesChiodo, Alessandro ;

University of Michigan

关键词: Landau-Ginzburg/Calabi-Yau Correspondence;    Mirror Symmetry;    Mathematics;    Science;    Mathematics;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/107147/priddisn_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

From High Energy Physics there is a certain expected correspondence between two different physical models, the Landau--Ginzburg model and the geometric or Calabi--Yau model. This correspondence is known as the Landau--Ginzburg/Calabi--Yau correspondence. The Landau--Ginzburg model has been recently developed mathematically, and goes by the name of FJRW theory. The Calabi--Yau model has been around much longer and is known mathematically as Gromov--Witten theory. The Landau--Ginzburg/Calabi--Yau correspondence therefore takes the form of a precise relationship between the Gromov--Witten theory of a Calabi--Yau variety and the FJRW theory for a certain related potential function. We state and prove the relationship for the famous ;;mirror quintic;;---a quotient of the quintic three--fold by a certain finite group. In the process we also prove a Landau--Ginzburg mirror theorem for the mirror quintic.