Dualities Arising from Borcea-Voisin Threefolds

Gromov-Witten;Mirror symmetry;Borcea-Voisin;Calabi-Yau;Orbifold;Landau-Ginzburg;Mathematics;Science;Mathematics

Schaug, AndrewFulton, William ;

University of Michigan

关键词: Gromov-Witten;    Mirror symmetry;    Borcea-Voisin;    Calabi-Yau;    Orbifold;    Landau-Ginzburg;    Mathematics;    Science;    Mathematics;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/138597/trygve_1.pdf?sequence=1&isAllowed=y

瑞士|英语

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

【 摘 要 】

In the early 1990s, Borcea-Voisin orbifolds were some of the earliest examples of Calabi-Yau threefolds shown to exhibit mirror symmetry, but at the quantum level this has been poorly understood. Here the enumerative geometry of this family is placed in the context of a gauged linear sigma model which encompasses the threefolds’ Gromov-Witten theory and three companion theories (FJRW theory and two mixed theories). For certain Borcea-Voisin orbifolds of Fermat type, all four genus zero theories are calculated explicitly. Furthermore, the I-functions of these theories are related by analytic continuation and symplectic transformation. In particular, it is shown that the relation between the Gromov-Witten and FJRW theories can be viewed as an example of the Landau-Ginzburg/Calabi-Yau correspondence for complete intersections of toric varieties. For certain mirror families, the corresponding Picard-Fuchs systems are then derived and the I-functions are shown to solve them, thus demonstrating that the mirror symmetry of Borcea-Voisin orbifolds extends to the quantum level.