Graded Contact Geometry and the AKSZ Formalism
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909925374951424 |
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| author | Contreras, Ivan Martinez-Alba, Nicolas Mehta, Rajan Amit |
| author_facet | Contreras, Ivan Martinez-Alba, Nicolas Mehta, Rajan Amit |
| contents | The AKSZ formalism is a construction of topological field theories where the target spaces are differential graded symplectic manifolds. In this paper, we describe an analogue of the AKSZ formalism where the target spaces are differential graded contact manifolds. We show that the space of fields inherits a weak contact structure, and we construct a solution to the analogue of the classical master equation, defined via the Jacobi bracket. In the $n=1$ case, we recover the Jacobi sigma model, and in the $n=2$ case, we obtain three-dimensional topological field theories associated to Courant-Jacobi algebroids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20789 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Graded Contact Geometry and the AKSZ Formalism Contreras, Ivan Martinez-Alba, Nicolas Mehta, Rajan Amit Mathematical Physics Symplectic Geometry 18B40, 58A50, 53D10, 57R56, 18B40, 58A50, 53D10, 57R56, 53D17 The AKSZ formalism is a construction of topological field theories where the target spaces are differential graded symplectic manifolds. In this paper, we describe an analogue of the AKSZ formalism where the target spaces are differential graded contact manifolds. We show that the space of fields inherits a weak contact structure, and we construct a solution to the analogue of the classical master equation, defined via the Jacobi bracket. In the $n=1$ case, we recover the Jacobi sigma model, and in the $n=2$ case, we obtain three-dimensional topological field theories associated to Courant-Jacobi algebroids. |
| title | Graded Contact Geometry and the AKSZ Formalism |
| topic | Mathematical Physics Symplectic Geometry 18B40, 58A50, 53D10, 57R56, 18B40, 58A50, 53D10, 57R56, 53D17 |
| url | https://arxiv.org/abs/2511.20789 |