A note on the quantization of M2-branes on local Calabi-Yau manifolds

Abstract

In this note we present a detailed computation of the BPS states from M2-branes wrapping 2-cycles in local Calabi-Yau manifolds, at the level of brane quantization. For the cases of local Calabi-Yau threefolds, the supersymmetric quantum mechanics is the 1d 𝒩=4 non-linear sigma model. We achieve systematic, physical interpretations of refined Gopakumar-Vafa (GV) invariants, first for the curve classes with fixed geometric genus, and then for curves whose geometric genus jumps. The BPS states of 5d 𝒩=1 superconformal field theories are interpreted from the local geometries, which are presented in a number of case studies. In particular, we compute the refined GV invariants for generalized conifolds, local CY3 giving 5d 𝒩=1 gauge theories and a singularity whose crepant resolution contains a singular divisor. For the cases of local Calabi-Yau fourfolds, we point out the supersymmetric quantum mechanics is of type 𝒩=2B. We set up the framework for studying M2-branes wrapping 2-cycles, and discuss a few cases of M2-brane wrapping genus-0 curves with this new approach.

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BibTeX RIS

BibTeX

@misc{huang2026note,
  title = {{A note on the quantization of M2-branes on local Calabi-Yau manifolds}},
  author = {Yutong Huang and Qinjian Lou and Jiahua Tian and Yi-Nan Wang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00687},
  eprint = {2611.00687},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00687},
}

RIS

TY  - UNPB
TI  - A note on the quantization of M2-branes on local Calabi-Yau manifolds
AU  - Yutong Huang
AU  - Qinjian Lou
AU  - Jiahua Tian
AU  - Yi-Nan Wang
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00687
UR  - https://arxiv.org/abs/2611.00687
AB  - In this note we present a detailed computation of the BPS states from M2-branes wrapping 2-cycles in local Calabi-Yau manifolds, at the level of brane quantization. For the cases of local Calabi-Yau threefolds, the supersymmetric quantum mechanics is the 1d 𝒩=4 non-linear sigma model. We achieve systematic, physical interpretations of refined Gopakumar-Vafa (GV) invariants, first for the curve classes with fixed geometric genus, and then for curves whose geometric genus jumps. The BPS states of 5d 𝒩=1 superconformal field theories are interpreted from the local geometries, which are presented in a number of case studies. In particular, we compute the refined GV invariants for generalized conifolds, local CY3 giving 5d 𝒩=1 gauge theories and a singularity whose crepant resolution contains a singular divisor. For the cases of local Calabi-Yau fourfolds, we point out the supersymmetric quantum mechanics is of type 𝒩=2B. We set up the framework for studying M2-branes wrapping 2-cycles, and discuss a few cases of M2-brane wrapping genus-0 curves with this new approach.
ER  -

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