A Landau–Ginzburg/Calabi–Yau correspondence for the mirror quintic
Annales de l'Institut Fourier, Volume 66 (2016) no. 3, p. 1045-1091

We prove a version of the Landau–Ginzburg/Calabi–Yau correspondence for the mirror quintic. In particular we calculate the genus–zero FJRW theory for the pair (W,G) where W is the Fermat quintic polynomial and G=SL W . We identify it with the Gromov–Witten theory of the mirror quintic three–fold via an explicit analytic continuation and symplectic transformation. In the process we prove a mirror theorem for the corresponding Landau–Ginzburg model (W,G).

Nous montrons une version de la correspondance Landau–Ginzburg/ Calabi–Yau pour le miroir quintique. Plus précisément, on calcule la théorie FJRW en genre zéro pour la paire (W,G), où W est le polynôme de Fermat quintique et G=SL W . On l’identifie ensuite avec la théorie de Gromov–Witten de la quintique avec une continuation analytique explicite et une transformation symplectique. On démontre au passage un théorème miroir pour le modèle de Landau–Ginzburg (W,G) correspondant.

Received : 2014-07-21
Accepted : 2015-10-08
Published online : 2016-12-14
DOI : https://doi.org/10.5802/aif.3031
Classification:  14N35,  14J33,  53D45,  14J17,  32G20
Keywords: Landau–Ginzburg, Calabi–Yau, Mirror symmetry
     author = {Priddis, Nathan and Shoemaker, Mark},
     title = {A Landau--Ginzburg/Calabi--Yau correspondence for the mirror quintic},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {66},
     number = {3},
     year = {2016},
     pages = {1045-1091},
     doi = {10.5802/aif.3031},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2016__66_3_1045_0}
Priddis, Nathan; Shoemaker, Mark. A Landau–Ginzburg/Calabi–Yau correspondence for the mirror quintic. Annales de l'Institut Fourier, Volume 66 (2016) no. 3, pp. 1045-1091. doi : 10.5802/aif.3031. http://www.numdam.org/item/AIF_2016__66_3_1045_0/

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