New Invariants for Non-Fano Manifolds from Cohomological Quantum Field Theory

by Michael Lathwood (University of New Hampshire)

Aula Conversi (Dip. di Fisica - Edificio G. Marconi)

Aula Conversi

Dip. di Fisica - Edificio G. Marconi


The topological A-model and topological B-model are topological quantum field theories which can be constructed with BRST cohomology. These theories only depend on only a Kähler or complex structure moduli space, respectively. Correlation functions in the topological A-model can be expressed in terms of Gromov-Witten invariants whereas the equivalent mirror topological B-model admits a simpler description in terms of period integrals. In this talk (based on arXiv:2404.16782), we solve the open/closed Picard-Fuchs system for the Hirzebruch surfaces, and hence compute periods to all orders of the mirror complex structure moduli on the B-side. We use toric degenerations, scattering diagrams, and Landau-Ginzburg models from the Gross-Siebert mirror symmetry program to compute Gromov-Witten invariants on the A-side. We observe novel features such as internal scattering in the non-Fano case. Following the work of Carl-Pumperla-Siebert, we compute corrected mirror superpotentials ϑ_1(𝔽_m) and their periods for the Hirzebruch surfaces 𝔽_m with m ≥ 2. This work extends the result of Gräfnitz-Ruddat-Zaslow. Namely, the proper Landau-Ginzburg superpotential is the open mirror map even in the non-Fano setting.

Organized by

Salvatore Ferrone