Chern-Simons potentials of higher-dimensional Pontryagin densities
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866918144401997824 |
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| author | Çakmak, Onur Ayberk Sarıoğlu, Özgür |
| author_facet | Çakmak, Onur Ayberk Sarıoğlu, Özgür |
| contents | We develop a novel and systematic approach to computing the $(2n-1)$-form Chern-Simons potential given the Pontryagin density, i.e. the $n^{\text{th}}$ Chern character, in arbitrary even dimensions $D=2 n \geq 2$. Throughout we work with a generic affine connection, that results in a non-vanishing torsion in general, and allows for non-metricity, which accommodates the existence of non-trivial Chern characters and hence Pontryagin densities. We outline an algorithm, with its implementation as a code, which lets one to determine the Chern-Simons potential given the Pontryagin density in an arbitrary even dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07461 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chern-Simons potentials of higher-dimensional Pontryagin densities Çakmak, Onur Ayberk Sarıoğlu, Özgür Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Theory Differential Geometry Geometric Topology We develop a novel and systematic approach to computing the $(2n-1)$-form Chern-Simons potential given the Pontryagin density, i.e. the $n^{\text{th}}$ Chern character, in arbitrary even dimensions $D=2 n \geq 2$. Throughout we work with a generic affine connection, that results in a non-vanishing torsion in general, and allows for non-metricity, which accommodates the existence of non-trivial Chern characters and hence Pontryagin densities. We outline an algorithm, with its implementation as a code, which lets one to determine the Chern-Simons potential given the Pontryagin density in an arbitrary even dimension. |
| title | Chern-Simons potentials of higher-dimensional Pontryagin densities |
| topic | Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Theory Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2505.07461 |