[Une correspondance Landau–Ginzburg/Calabi–Yau pour le miroir quintique]
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 , où est le polynôme de Fermat quintique et . 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 correspondant.
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 where is the Fermat quintic polynomial and . 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 .
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Keywords: Landau–Ginzburg, Calabi–Yau, Mirror symmetry
Mot clés : Landau–Ginzburg, Calabi–Yau, la symétrie miroir
@article{AIF_2016__66_3_1045_0,
author = {Priddis, Nathan and Shoemaker, Mark},
title = {A {Landau{\textendash}Ginzburg/Calabi{\textendash}Yau} correspondence for the mirror quintic},
journal = {Annales de l'Institut Fourier},
pages = {1045--1091},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {66},
number = {3},
year = {2016},
doi = {10.5802/aif.3031},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.3031/}
}
TY - JOUR AU - Priddis, Nathan AU - Shoemaker, Mark TI - A Landau–Ginzburg/Calabi–Yau correspondence for the mirror quintic JO - Annales de l'Institut Fourier PY - 2016 SP - 1045 EP - 1091 VL - 66 IS - 3 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.3031/ DO - 10.5802/aif.3031 LA - en ID - AIF_2016__66_3_1045_0 ER -
%0 Journal Article %A Priddis, Nathan %A Shoemaker, Mark %T A Landau–Ginzburg/Calabi–Yau correspondence for the mirror quintic %J Annales de l'Institut Fourier %D 2016 %P 1045-1091 %V 66 %N 3 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.3031/ %R 10.5802/aif.3031 %G en %F 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, Tome 66 (2016) no. 3, pp. 1045-1091. doi : 10.5802/aif.3031. http://www.numdam.org/articles/10.5802/aif.3031/
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