Twisted Gromov-Witten r-spin potential and Givental's quantization

Abstract

The universal curve p:C->\Mbar over the moduli space \Mbar of stable r-spin maps to a target Kähler manifold X carries a universal spinor bundle L->C. Therefore the moduli space \Mbar itself carries a natural K-theory class Rp_*L. We introduce a twisted r-spin Gromov-Witten potential of X enriched with Chern characters of Rp_*L. We show that the twisted potential can be reconstructed from the ordinary r-spin Gromov-Witten potential of X via an operator that assumes a particularly simple form in Givental's quantization formalism.

25 pages, 3 figures

References in corpus (5)

• Tautological relations and the r-spin Witten conjecture
• Orbifold Quantum Riemann-Roch, Lefschetz and Serre
• Computing Genus-Zero Twisted Gromov-Witten Invariants
• Constructions of nontautological classes on moduli spaces of curves
• Witten's top Chern class via K-theory

Cited by in corpus (5)

• Landau-Ginzburg/Calabi-Yau correspondence for quintic three-folds via symplectic transformations
• Equivalence of ELSV and Bouchard-Mariño conjectures for $r$-spin Hurwitz numbers
• Givental symmetries of Frobenius manifolds and multi-component KP tau-functions
• A group action on Losev-Manin cohomological field theories
• A global mirror symmetry framework for the Landau-Ginzburg/Calabi-Yau correspondence