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PreprintCC BY 4.0arXiv

A local action for Kodaira--Spencer gravity

  • Olaf Hohm
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Abstract

A local action is given for Kodaira--Spencer gravity by solving a constraint on the complex structure deformation of a Calabi--Yau threefold in terms of a (1,1) form as the new gravity field. The gauge algebra becomes a genuine L∞ algebra based on a Courant algebroid, while the gravity field and its linearized gauge transformations coincide with those of double field theory. On a real three-dimensional slice, the free action reduces to the Fierz--Pauli action for massless spin-2 plus the Kalb--Ramond action for a B-field. Non-linearly, the theory carries parity-odd interactions with three derivatives, and it is gauge invariant without a level-matching constraint, in this sense defining an unconstrained double field theory. The full theory is encoded in a cyclic L∞ algebra, for which a double copy interpretation is given.

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Cite

BibTeXRIS
BibTeX
@misc{hohm2026local,
  title = {{A local action for Kodaira--Spencer gravity}},
  author = {Olaf Hohm},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00213},
  eprint = {2611.00213},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00213},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A local action for Kodaira--Spencer gravity
AU  - Olaf Hohm
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00213
UR  - https://arxiv.org/abs/2611.00213
AB  - A local action is given for Kodaira--Spencer gravity by solving a constraint on the complex structure deformation of a Calabi--Yau threefold in terms of a (1,1) form as the new gravity field. The gauge algebra becomes a genuine L_∞ algebra based on a Courant algebroid, while the gravity field and its linearized gauge transformations coincide with those of double field theory. On a real three-dimensional slice, the free action reduces to the Fierz--Pauli action for massless spin-2 plus the Kalb--Ramond action for a B-field. Non-linearly, the theory carries parity-odd interactions with three derivatives, and it is gauge invariant without a level-matching constraint, in this sense defining an unconstrained double field theory. The full theory is encoded in a cyclic L_∞ algebra, for which a double copy interpretation is given.
ER  -