Gromov-Witten invariants of target curves via Symplectic Field Theory

Abstract

We compute the Gromov-Witten potential at all genera of target smooth Riemann surfaces using Symplectic Field Theory techniques and establish differential equations for the full descendant potential. This amounts to impose (and possibly solve) different kinds of Schroedinger equations related to some quantization of the dispersionless KdV hierarchy. In particular we find very explicit formulas for the Gromov-Witten invariants of low degree of P1 with descendants of the Kaehler class.

arXiv comment13 pages

References in corpus (3)

• Holomorphic Anomalies in Topological Field Theories
• Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants
• Quantum Cohomology and Virasoro Algebra

Cited by in corpus (13)

• Integrals of psi-classes over double ramification cycles
• Ramifications of Hurwitz theory, KP integrability and quantum curves
• Equivariant Gromov-Witten theory of one dimensional stacks
• Loop equations and a proof of Zvonkine's $qr$-ELSV formula
• Sekiguchi-Debiard operators at infinity
• On Elliptic Algebras and Large-n Supersymmetric Gauge Theories
• Quantum Hydrodynamics from Large-n Supersymmetric Gauge Theories
• Integrability, Quantization and Moduli Spaces of Curves
• Gromov-Witten theory of orbicurves, the space of tri-polynomials and Symplectic Field Theory of Seifert fibrations
• Special cases of the orbifold version of Zvonkine's $r$-ELSV formula
• Topological recursion for monotone orbifold Hurwitz numbers: a proof of the Do-Karev conjecture
• On the spectral problem of the quantum KdV hierarchy
• Quantum KdV hierarchy and shifted symmetric functions