Kodaira-Spencer theory for Courant algebroids
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arXiv
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| Format: | Preprint |
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2026
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| author | Kupka, Julian Saberi, Ingmar Strickland-Constable, Charles Valach, Fridrich |
| author_facet | Kupka, Julian Saberi, Ingmar Strickland-Constable, Charles Valach, Fridrich |
| contents | Studying Courant algebroids on dg ringed manifolds, we observe that the associated Roytenberg-Weinstein $L_\infty$ algebra admits a local structure reminiscent of a shifted contact structure. On a dg ringed manifold with an $n$-orientation, its symplectification produces a sheaf of $(2-n)$-shifted symplectic formal moduli problems, which we call the Courant contact model. This construction can be interpreted as a ($\mathbb{Z}/2\mathbb{Z}$-graded) theory in the Batalin-Vilkovisky formalism whenever $n$ is odd. After developing the procedure of reduction and extension of scalars, we show how twisted backgrounds in type I supergravity naturally lead to Courant algebroids over the Dolbeault complex. Specialising to the case of a Calabi-Yau fivefold, we show that the Courant contact model for that Courant algebroid is equivalent to a central extension of minimal type I BCOV theory. Inspired by this, we extend the conjecture of Costello and Li and place it within the setting of generalized geometry, conjecturing a description of the BV formulation of type I supergravity in general twisted backgrounds. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_04658 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Kodaira-Spencer theory for Courant algebroids Kupka, Julian Saberi, Ingmar Strickland-Constable, Charles Valach, Fridrich Mathematical Physics High Energy Physics - Theory Symplectic Geometry 53D18, 58H15, 32G13, 83E50 Studying Courant algebroids on dg ringed manifolds, we observe that the associated Roytenberg-Weinstein $L_\infty$ algebra admits a local structure reminiscent of a shifted contact structure. On a dg ringed manifold with an $n$-orientation, its symplectification produces a sheaf of $(2-n)$-shifted symplectic formal moduli problems, which we call the Courant contact model. This construction can be interpreted as a ($\mathbb{Z}/2\mathbb{Z}$-graded) theory in the Batalin-Vilkovisky formalism whenever $n$ is odd. After developing the procedure of reduction and extension of scalars, we show how twisted backgrounds in type I supergravity naturally lead to Courant algebroids over the Dolbeault complex. Specialising to the case of a Calabi-Yau fivefold, we show that the Courant contact model for that Courant algebroid is equivalent to a central extension of minimal type I BCOV theory. Inspired by this, we extend the conjecture of Costello and Li and place it within the setting of generalized geometry, conjecturing a description of the BV formulation of type I supergravity in general twisted backgrounds. |
| title | Kodaira-Spencer theory for Courant algebroids |
| topic | Mathematical Physics High Energy Physics - Theory Symplectic Geometry 53D18, 58H15, 32G13, 83E50 |
| url | https://arxiv.org/abs/2602.04658 |