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.

Typos corrected and exposition improved. 40 pages

References in corpus (2)

• Mixed-Spin-P fields of Fermat quintic polynomials
• Torus localization and wall crossing for cosection localized virtual cycles

Cited by in corpus (2)

• A mirror theorem for genus two Gromov-Witten invariants of quintic threefolds
• Structure of Higher Genus Gromov-Witten Invariants of Quintic 3-folds