Non-associative Algebras of Cubic Matrices and their Gauge Theories
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917980494888960 |
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| author | Blumenhagen, Ralph Paraskevopoulou, Antonia Raml, Thomas |
| author_facet | Blumenhagen, Ralph Paraskevopoulou, Antonia Raml, Thomas |
| contents | Motivated by M-theory, we define a new type of non-associative algebra involving usual and cubic matrices at the same time. The resulting algebra can be regarded as a two-term truncated $L_\infty$ algebra giving rise to a fundamental identity between the two- and the three-bracket. We provide a simple class of concrete examples of such algebras based on the structure constants of a Lie algebra. Connecting to previous results on higher structures, we generalize the construction of Yang-Mills theories, topological BF theory and generalized IKKT models and point out some appearing issues. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02942 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-associative Algebras of Cubic Matrices and their Gauge Theories Blumenhagen, Ralph Paraskevopoulou, Antonia Raml, Thomas High Energy Physics - Theory Mathematical Physics Motivated by M-theory, we define a new type of non-associative algebra involving usual and cubic matrices at the same time. The resulting algebra can be regarded as a two-term truncated $L_\infty$ algebra giving rise to a fundamental identity between the two- and the three-bracket. We provide a simple class of concrete examples of such algebras based on the structure constants of a Lie algebra. Connecting to previous results on higher structures, we generalize the construction of Yang-Mills theories, topological BF theory and generalized IKKT models and point out some appearing issues. |
| title | Non-associative Algebras of Cubic Matrices and their Gauge Theories |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2504.02942 |