Extended Bargmann FDA and non-relativistic gravity
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913769192423424 |
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| author | Muñoz, Ariana Rubio, Gustavo Salgado, Sebastián |
| author_facet | Muñoz, Ariana Rubio, Gustavo Salgado, Sebastián |
| contents | In this paper we consider the construction of a free differential algebra as an extension of the extended Bargmann algebra in arbitrary dimensions. This is achieved by introducing a new Maurer-Cartan equation for a three-form gauge multiplet in the adjoint representation of the extended Bargmann algebra. The new Maurer-Cartan equation is provided of non-triviality by means of the introduction of a four-form cocycle, representative of a Chevalley-Eilenberg cohomology class. We derive the corresponding dual $L_{\infty}$ algebra and, by using the formalism of non-linear realizations, propose a five-dimensional gauge invariant action principle. Then, we derive the corresponding equations of motion and study how the presence of the three-form gauge fields and the four-cocycle modify the corresponding non-relativistic dynamics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_00140 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extended Bargmann FDA and non-relativistic gravity Muñoz, Ariana Rubio, Gustavo Salgado, Sebastián High Energy Physics - Theory General Relativity and Quantum Cosmology In this paper we consider the construction of a free differential algebra as an extension of the extended Bargmann algebra in arbitrary dimensions. This is achieved by introducing a new Maurer-Cartan equation for a three-form gauge multiplet in the adjoint representation of the extended Bargmann algebra. The new Maurer-Cartan equation is provided of non-triviality by means of the introduction of a four-form cocycle, representative of a Chevalley-Eilenberg cohomology class. We derive the corresponding dual $L_{\infty}$ algebra and, by using the formalism of non-linear realizations, propose a five-dimensional gauge invariant action principle. Then, we derive the corresponding equations of motion and study how the presence of the three-form gauge fields and the four-cocycle modify the corresponding non-relativistic dynamics. |
| title | Extended Bargmann FDA and non-relativistic gravity |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2504.00140 |