SciPost Submission Page
Revisiting the Quantum Geometry of Torus-fibered Calabi-Yau Threefolds
by Boris Pioline, Thorsten Schimannek
Submission summary
| Authors (as registered SciPost users): | Thorsten Schimannek |
| Submission information | |
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| Preprint Link: | scipost_202601_00060v1 (pdf) |
| Date submitted: | Jan. 26, 2026, 10:10 a.m. |
| Submitted by: | Thorsten Schimannek |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
About ten years ago, Katz, Klemm and Huang conjectured that topological string amplitudes on compact, elliptically fibered Calabi-Yau threefolds at fixed base degree could be expressed in terms of meromorphic Jacobi forms for SL(2,ℤ), giving access to Gromov-Witten invariants at arbitrary genus. This was later generalized to torus-fibered CY threefolds with N-sections, where topological string amplitudes are conjecturally governed by meromorphic Jacobi forms under the congruence subgroup Γ1(N). In this work, we show that these modularity properties follow from (and are equivalent to) the wave-function property of the topological string partition function Ztop under a relative conifold monodromy, implementing a particular Fourier-Mukai transformation on the derived category of coherent sheaves. In particular, we introduce a variant of Ztop which is both holomorphic and modular covariant. Under the same relative conifold monodromy, the generating series of genus 0 Gopakumar-Vafa invariants at fixed base degree is mapped to the generating series of rank 0 Donaldson-Thomas indices counting D4-D2-D0-brane bound states wrapped on the torus fiber. We show that the quasimodularity of the generating series of GV invariants matches the expected mock-modular behavior of the generating series of D4-D2-D0 indices, despite having different multi-cover contributions. We analyze and tabulate a large number of CY threefolds fibered over del Pezzo surfaces, with an N-section for N≤5, including several new examples beyond the realm of toric geometry.
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