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

Abstract

We study the equivariantly perturbed mirror Landau-Ginzburg model of the projective line. We show that the Eynard-Orantin recursion on this model encodes all genus all descendants equivariant Gromov-Witten invariants of the projective line. The non-equivariant limit of this result is the Norbury-Scott conjecture, while by taking large radius limit we recover the Bouchard-Marino conjecture on simple Hurwitz numbers.

34 pages, 5 figures; references added, typos corrected

References in corpus (7)

• Symplectic invariants, Virasoro constraints and Givental decomposition
• The equivariant Gromov-Witten theory of P^1
• CFT and topological recursion
• Polynomiality of Hurwitz numbers, Bouchard-Mariño conjecture, and a new proof of the ELSV formula
• Quantum spectral curve for the Gromov-Witten theory of the complex projective line
• All Genus Open-Closed Mirror Symmetry for Affine Toric Calabi-Yau 3-Orbifolds
• Gromov-- Witten Invariants of Toric Fibrations

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• Gromov-Witten invariants of ${\mathbb{P}}^1$ coupled to a KdV tau function
• Taking limits in topological recursion
• Topological recursion of Eynard-Orantin and the Harmonic Oscillator
• Virasoro Constraints of Curves as Residues
• Equivariant mirror symmetry for the weighted projective line
• Topological recursion on transalgebraic spectral curves and Atlantes Hurwitz numbers
• Generalisations of the Harer-Zagier recursion for 1-point functions
• Quantum curve and bilinear Fermionic form for the orbifold Gromov-Witten theory of $\mathbb{P}[r]$
• A new spin on polynomial relations among kappa classes
• Primitive forms and Frobenius structures on the Hurwitz spaces