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PreprintCC BY 4.0arXiv

Morse Index of a G2-Instanton over S7

  • Xiaoli Han
  • Yang Wen
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Abstract

In this paper, we determine the nonpositive spectrum of the Yang-Mills Jacobi operator in Coulomb gauge at the standard G2-instanton on S7. We prove that the only negative eigenvalue is −3, with multiplicity $8$, and the kernel has dimension $20$. Thus the connection attains the sharp lower bound for the Morse index of nonflat Yang-Mills connections on S7. We also give an explicit description of the kernal of the Jacobi operator, which contains Waldron's $15$-dimensional deformation space for the fixed nearly parallel G2-structure. The 5 additional zero modes are isometry-induced variations that do not satisfy the corresponding linearized instanton equation.

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Cite

BibTeXRIS
BibTeX
@misc{han2026morse,
  title = {{Morse Index of a $G_2$-Instanton over $S^7$}},
  author = {Xiaoli Han and Yang Wen},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.14369},
  eprint = {2609.14369},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14369},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Morse Index of a G_2-Instanton over S^7
AU  - Xiaoli Han
AU  - Yang Wen
PY  - 2026
DA  - 2026/10/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.14369
UR  - https://arxiv.org/abs/2609.14369
AB  - In this paper, we determine the nonpositive spectrum of the Yang-Mills Jacobi operator in Coulomb gauge at the standard G_2-instanton on S^7. We prove that the only negative eigenvalue is −3, with multiplicity $8$, and the kernel has dimension $20$. Thus the connection attains the sharp lower bound for the Morse index of nonflat Yang-Mills connections on S^7. We also give an explicit description of the kernal of the Jacobi operator, which contains Waldron's $15$-dimensional deformation space for the fixed nearly parallel G_2-structure. The 5 additional zero modes are isometry-induced variations that do not satisfy the corresponding linearized instanton equation.
ER  -