Meromorphic open-string vertex algebras and twisted modules from Courant algebroids
Abstract
We construct a sheaf of 1/2ℤ-graded meromorphic open-string vertex algebras from a transitive Courant algebroid E equipped with a generalized metric and a chosen generalized Levi-Civita connection on a smooth manifold. Using a holonomy principle for transitive anchored bundles, we realize these algebras as parallel sections of a tensor algebra bundle built from bosonic-fermionic affinizations of E. For even-rank E with suitable Clifford module bundle data, we construct a sheaf of canonically twisted modules containing the canonical weighted spinor bundle in weight zero. The associative algebra of parallel tensors acts on spinor sections through iterates of an E-connection combining covariant differentiation and Clifford multiplication, with mixed terms incorporating the action of the bosonic connection on fermionic tensors. Distinguished states built from the inverse Courant pairing and inverse generalized metric give vertex-operator components, acting on embedded spinor sections as the canonical Dirac generating operator, its formal adjoint, and their anticommutator, the generalized Hodge Laplacian. In the exact Courant case with three-form H and the exterior algebra Clifford module, the operators specialize to d−H∧, its adjoint, and the twisted Hodge Laplacian, reducing to the ordinary de Rham and Hodge operators when H=0. This extends the vertex-operator realization of geometric differential operators from functions to weighted spinors and differential forms, within the program of studying two-dimensional supersymmetric nonlinear sigma models.
Related
- Homological reduction of Courant algebroids
- Deformations of generalized complex structures on 𝒢-flat transitive Courant algebroids
- Toward Shifted symplectic Chiralization: Deformation of Courant Algebroids
- Lie algebroids are curved Lie algebras
- One-periodic category of twisted complexes, Cohen-Macaulay modules and differential modules
BibTeX
@misc{fang2026meromorphic,
title = {{Meromorphic open-string vertex algebras and twisted modules from Courant algebroids}},
author = {Qixuan Fang and Fei Qi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36370},
eprint = {2609.36370},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36370},
}
RIS
TY - UNPB
TI - Meromorphic open-string vertex algebras and twisted modules from Courant algebroids
AU - Qixuan Fang
AU - Fei Qi
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36370
UR - https://arxiv.org/abs/2609.36370
AB - We construct a sheaf of 1/2ℤ-graded meromorphic open-string vertex algebras from a transitive Courant algebroid E equipped with a generalized metric and a chosen generalized Levi-Civita connection on a smooth manifold. Using a holonomy principle for transitive anchored bundles, we realize these algebras as parallel sections of a tensor algebra bundle built from bosonic-fermionic affinizations of E. For even-rank E with suitable Clifford module bundle data, we construct a sheaf of canonically twisted modules containing the canonical weighted spinor bundle in weight zero. The associative algebra of parallel tensors acts on spinor sections through iterates of an E-connection combining covariant differentiation and Clifford multiplication, with mixed terms incorporating the action of the bosonic connection on fermionic tensors. Distinguished states built from the inverse Courant pairing and inverse generalized metric give vertex-operator components, acting on embedded spinor sections as the canonical Dirac generating operator, its formal adjoint, and their anticommutator, the generalized Hodge Laplacian. In the exact Courant case with three-form H and the exterior algebra Clifford module, the operators specialize to d−H∧, its adjoint, and the twisted Hodge Laplacian, reducing to the ordinary de Rham and Hodge operators when H=0. This extends the vertex-operator realization of geometric differential operators from functions to weighted spinors and differential forms, within the program of studying two-dimensional supersymmetric nonlinear sigma models.
ER -