Higher-genus Landau–Ginzburg/Saito–Givental mirror symmetry

Let WW be a nondegenerate polynomial and set G=Aut(W)G=\operatorname{Aut}(W). Let W0=WW^{\vee}_0=W^{\vee} be the Gepner point, let FFJRWg\mathcal F^g_{\operatorname{FJRW}} be the genus-gg FJRW potential, and let Fformalg\mathcal F^g_{\operatorname{formal}} be the genus-gg formal Saito–Givental potential. LG/LG higher-genus mirror symmetry. There is a mirror map matching a neighborhood of

HW,G1,1\mathcal H^{1,1}_{W,G}

with a neighborhood of W0W^{\vee}_0 such that the FFJRWg\mathcal F^g_{\operatorname{FJRW}}-function is matched to Fformalg\mathcal F^g_{\operatorname{formal}}. This is the Landau–Ginzburg counterpart of the preceding higher-genus Calabi–Yau conjecture; the source gives no general proof.

Sources & referencesView supporting material

Primary source

Alessandro Chiodo and Yongbin Ruan, “A global mirror symmetry framework for the Landau-Ginzburg/Calabi-Yau correspondence”, arXiv:1307.0939 (2013).

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