Genus-One Mirror Symmetry in the Landau-Ginzburg Model

Abstract

We prove an explicit formula for the genus-one Fan-Jarvis-Ruan-Witten invariants associated to the quintic threefold, verifying the genus-one mirror conjecture of Huang, Klemm, and Quackenbush. The proof involves two steps. The first step uses localization on auxiliary moduli spaces to compare the usual Fan-Jarvis-Ruan-Witten invariants with a semisimple theory of twisted invariants. The second step uses the genus-one formula for semisimple cohomological field theories to compute the twisted invariants explicitly.

arXiv commentTypos corrected and exposition improved. 40 pages

References in corpus (8)

• Phases of $N=2$ Theories In Two Dimensions
• The moduli space of stable quotients
• Landau-Ginzburg/Calabi-Yau correspondence for quintic three-folds via symplectic transformations
• A Mirror Theorem for Toric Stacks
• Elliptic Gromov - Witten invariants and the generalized mirror conjecture
• Mixed-Spin-P fields of Fermat quintic polynomials
• Higher genus quasimap wall-crossing for semi-positive targets
• Torus localization and wall crossing for cosection localized virtual cycles

Cited by in corpus (6)

• A mirror theorem for genus two Gromov-Witten invariants of quintic threefolds
• Structure of Higher Genus Gromov-Witten Invariants of Quintic 3-folds
• Polynomial structure of Gromov-Witten potential of quintic $3$-folds via NMSP
• Crepant resolution and the holomorphic anomaly equation for C^3/Z_3
• Quasimap wall-crossing for GIT quotients
• Higher-genus wall-crossing in Landau-Ginzburg theory