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Ricci-flat string algebroids
Abstract
We investigate geometric structures defined by 4-forms, encompassing important classes of geometric structures with torsion including almost Hermitian, G2, Spin(7), and almost quaternion/hyper Hermitian. Within this unified framework, the underlying 4-form naturally determines geometric data that define a string algebroid over the manifold. In particular, it gives rise to a canonical notion of instanton, thereby linking these geometries to gauge-theoretic structures in generalized geometry and heterotic string theory. We further prove that these data induce generalized Ricci-flat metrics. Finally, we examine the main examples in the literature and construct several explicit ones.
Related
- Deformations of generalized complex structures on 𝒢-flat transitive Courant algebroids
- Meromorphic open-string vertex algebras and twisted modules from Courant algebroids
- On complete Ricci--flat Kähler manifolds
- Instability of the Fundamental Group for Ricci-Flat Kähler 4-Manifolds
- Hamiltonian stationary Lagrangian currents in Ricci-flat Kähler manifolds
BibTeX
@misc{jr2026ricciflat,
title = {{Ricci-flat string algebroids}},
author = {Agnaldo A. da Silva Jr. and Henrique N. Sá Earp and Bernardo S. Vieira},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.22455},
eprint = {2608.22455},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.22455},
}
RIS
TY - UNPB
TI - Ricci-flat string algebroids
AU - Agnaldo A. da Silva Jr.
AU - Henrique N. Sá Earp
AU - Bernardo S. Vieira
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2608.22455
UR - https://arxiv.org/abs/2608.22455
AB - We investigate geometric structures defined by 4-forms, encompassing important classes of geometric structures with torsion including almost Hermitian, G_2, Spin(7), and almost quaternion/hyper Hermitian. Within this unified framework, the underlying 4-form naturally determines geometric data that define a string algebroid over the manifold. In particular, it gives rise to a canonical notion of instanton, thereby linking these geometries to gauge-theoretic structures in generalized geometry and heterotic string theory. We further prove that these data induce generalized Ricci-flat metrics. Finally, we examine the main examples in the literature and construct several explicit ones.
ER -