The Eynard–Orantin recursion and equivariant mirror symmetry for the projective line

Fang, Bohan¹ ; Liu, Chiu-Chu² ; Zong, Zhengyu³

¹ Beijing International Center for Mathematical Research, Peking University, 5 Yiheyuan Road, Jingchunyuan 78, Beijing, 100871, China
² Department of Mathematics, Columbia University, Room 623, Mail Code 4435, 2990 Broadway, New York, NY 10027, United States
³ Yau Mathematical Sciences Center, Tsinghua University, Jing Chun Yuan West Building, Tsinghua University, Haidian District, Beijing, 100084, China

Geometry & topology, Tome 21 (2017) no. 4, pp. 2049-2092.

Résumé

We study the equivariantly perturbed mirror Landau–Ginzburg model of ${\mathbb{P}}^1$. We show that the Eynard–Orantin recursion on this model encodes all-genus, all-descendants equivariant Gromov–Witten invariants of ${\mathbb{P}}^1$. The nonequivariant limit of this result is the Norbury–Scott conjecture, while by taking large radius limit we recover the Bouchard–Mariño conjecture on simple Hurwitz numbers.

Détail

DOI : 10.2140/gt.2017.21.2049

Classification : 14N35
Keywords: Gromov–Witten invariants, mirror symmetry, Eynard–Orantin recursion, Norbury–Scott conjecture

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