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Membranes and Maps

  • Alessandro Giacchetto
  • Rahul Pandharipande
  • Yannik Schuler
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Abstract

In positive degree, equivariant Gromov-Witten invariants of Calabi-Yau fivefolds are expected to admit an interpretation in terms of M2-branes, while we conjecture that constant maps are governed by the corresponding supergravity index. We make the first expectation precise by proposing a modular interpretation of M2-branes supported on several smooth curves meeting at an n-fold point. Together, the two pictures yield conjectural formulas for the Gromov-Witten invariants, which we translate into closed formulas for pointed and unpointed quintuple Hodge integrals. We show that these conjectures imply a K-theoretic Gromov-Witten/Pairs correspondence for local curves in degree one and link the generating series of constant maps to Donaldson-Thomas theory of points. We also prove the conjectures in two limits of the equivariant parameters. Along the way, we obtain new closed formulas for certain triple Hodge integrals.

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Cite

BibTeXRIS
BibTeX
@misc{giacchetto2026membranes,
  title = {{Membranes and Maps}},
  author = {Alessandro Giacchetto and Rahul Pandharipande and Yannik Schuler},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.02409},
  eprint = {2609.02409},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.02409},
}
RIS
TY  - UNPB
TI  - Membranes and Maps
AU  - Alessandro Giacchetto
AU  - Rahul Pandharipande
AU  - Yannik Schuler
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2609.02409
UR  - https://arxiv.org/abs/2609.02409
AB  - In positive degree, equivariant Gromov-Witten invariants of Calabi-Yau fivefolds are expected to admit an interpretation in terms of M2-branes, while we conjecture that constant maps are governed by the corresponding supergravity index. We make the first expectation precise by proposing a modular interpretation of M2-branes supported on several smooth curves meeting at an n-fold point. Together, the two pictures yield conjectural formulas for the Gromov-Witten invariants, which we translate into closed formulas for pointed and unpointed quintuple Hodge integrals. We show that these conjectures imply a K-theoretic Gromov-Witten/Pairs correspondence for local curves in degree one and link the generating series of constant maps to Donaldson-Thomas theory of points. We also prove the conjectures in two limits of the equivariant parameters. Along the way, we obtain new closed formulas for certain triple Hodge integrals.
ER  -