Quantum spectral curve for the Gromov-Witten theory of the complex projective line

Abstract

We construct the quantum curve for the Gromov-Witten theory of the complex projective line.

arXiv comment33 pages

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• The Eynard-Orantin recursion and equivariant mirror symmetry for the projective line
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• Topological recursion and a quantum curve for monotone Hurwitz numbers
• Quantization of Harer-Zagier formulas
• From CFT to Ramond super-quantum curves
• Cut-and-join equation for monotone Hurwitz numbers revisited
• An algebraic approach to a quartic analogue of the Kontsevich model
• Quantum curves for the enumeration of ribbon graphs and hypermaps
• Quantizing Weierstrass
• WKB solutions of difference equations and reconstruction by the topological recursion
• Topological recursion and uncoupled BPS structures II: Voros symbols and the $\tau$-function
• Matrix Field Theory
• Reconstructing GKZ via topological recursion
• Gromov-Witten invariants of ${\mathbb{P}}^1$ coupled to a KdV tau function
• Interplay between opers, quantum curves, WKB analysis, and Higgs bundles
• Quantization of classical spectral curves via topological recursion
• Topological recursion and uncoupled BPS structures I: BPS spectrum and free energies
• Topological recursion of Eynard-Orantin and the Harmonic Oscillator
• 4D limit of melting crystal model and its integrable structure
• Matrix model for the stationary sector of Gromov-Witten theory of ${\mathbf{P}}^1$
• Quantum curve and bilinear Fermionic form for the orbifold Gromov-Witten theory of $\mathbb{P}[r]$