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Exact Nambu-Goto 4-Surfaces and Octonionic Cayley Selection in 8D

  • Graeme Donald Robertson
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Abstract

We study four-dimensional Euclidean Nambu-Goto embeddings in eight dimensions in the presence of the Spin(7)-invariant four-form constructed from octonionic structure constants. A broad class of holomorphic maps is shown by direct substitution to satisfy the nonlinear Nambu-Goto Euler-Lagrange equations. For a compatible Spin(7) structure these same embeddings satisfy the Cayley calibration condition. The calculation therefore gives a discrete octonionic selection rule for the relative orientation of an exact Nambu-Goto 4-surface and the Spin(7) structure of the target.

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Cite

BibTeXRIS
BibTeX
@misc{robertson2026exact,
  title = {{Exact Nambu-Goto 4-Surfaces and Octonionic Cayley Selection in 8D}},
  author = {Graeme Donald Robertson},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.22775},
  eprint = {2607.22775},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.22775},
}
RIS
TY  - UNPB
TI  - Exact Nambu-Goto 4-Surfaces and Octonionic Cayley Selection in 8D
AU  - Graeme Donald Robertson
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2607.22775
UR  - https://arxiv.org/abs/2607.22775
AB  - We study four-dimensional Euclidean Nambu-Goto embeddings in eight dimensions in the presence of the Spin(7)-invariant four-form constructed from octonionic structure constants. A broad class of holomorphic maps is shown by direct substitution to satisfy the nonlinear Nambu-Goto Euler-Lagrange equations. For a compatible Spin(7) structure these same embeddings satisfy the Cayley calibration condition. The calculation therefore gives a discrete octonionic selection rule for the relative orientation of an exact Nambu-Goto 4-surface and the Spin(7) structure of the target.
ER  -