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 with 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.