Geodesic
Partition functions of $\mathcal{N}=(2,2)$ supersymmetric sigma models and special geometry on the~moduli spaces of Calabi--Yau manifolds
Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 2, pp. 222-231

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We study a new example of a mirror relation between the exact partition functions of $\mathcal{N}{=}(2,2)$ supersymmetric gauged linear sigma models on the sphere $S^2$ and the special Kähler geometry on the moduli spaces of Calabi–Yau manifolds. Using exact calculations, we show this relation indeed holds for Calabi–Yau manifolds of the Berglund–Hubsch type with two moduli.
Keywords: superstring theory, moduli space of Calabi–Yau manifolds, special geometry.
Mots-clés : compactification 
@article{TMF_2019_201_2_a5,
     author = {A. A. Belavin and B. A. Eremin},
     title = {Partition functions of $\mathcal{N}=(2,2)$ supersymmetric sigma models and special geometry on the~moduli spaces of {Calabi--Yau} manifolds},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {222--231},
     publisher = {mathdoc},
     volume = {201},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_201_2_a5/}
}
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A. A. Belavin; B. A. Eremin. Partition functions of $\mathcal{N}=(2,2)$ supersymmetric sigma models and special geometry on the~moduli spaces of Calabi--Yau manifolds. Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 2, pp. 222-231. http://geodesic.mathdoc.fr/item/TMF_2019_201_2_a5/