Brane mechanics and gapped Lie n-algebroids
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| Format: | Preprint |
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2024
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| _version_ | 1866909177519013888 |
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| author | Chatzistavrakidis, Athanasios Kodžoman, Toni Škoda, Zoran |
| author_facet | Chatzistavrakidis, Athanasios Kodžoman, Toni Škoda, Zoran |
| contents | We draw a parallel between the BV/BRST formalism for higher-dimensional ($\ge 2$) Hamiltonian mechanics and higher notions of torsion and basic curvature tensors for generalized connections in specific Lie $n$-algebroids based on homotopy Poisson structures. The gauge systems we consider include Poisson sigma models in any dimension and ``generalised R-flux'' deformations thereof, such as models with an $(n+2)$-form-twisted R-Poisson target space. Their BV/BRST action includes interaction terms among the fields, ghosts and antifields whose coefficients acquire a geometric meaning by considering twisted Koszul multibrackets that endow the target space with a structure that we call a gapped almost Lie $n$-algebroid. Studying covariant derivatives along $n$-forms, we define suitable polytorsion and basic polycurvature tensors and identify them with the interaction coefficients in the gauge theory, thus relating models for topological $n$-branes to differential geometry on Lie $n$-algebroids. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_14126 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Brane mechanics and gapped Lie n-algebroids Chatzistavrakidis, Athanasios Kodžoman, Toni Škoda, Zoran High Energy Physics - Theory Mathematical Physics Differential Geometry We draw a parallel between the BV/BRST formalism for higher-dimensional ($\ge 2$) Hamiltonian mechanics and higher notions of torsion and basic curvature tensors for generalized connections in specific Lie $n$-algebroids based on homotopy Poisson structures. The gauge systems we consider include Poisson sigma models in any dimension and ``generalised R-flux'' deformations thereof, such as models with an $(n+2)$-form-twisted R-Poisson target space. Their BV/BRST action includes interaction terms among the fields, ghosts and antifields whose coefficients acquire a geometric meaning by considering twisted Koszul multibrackets that endow the target space with a structure that we call a gapped almost Lie $n$-algebroid. Studying covariant derivatives along $n$-forms, we define suitable polytorsion and basic polycurvature tensors and identify them with the interaction coefficients in the gauge theory, thus relating models for topological $n$-branes to differential geometry on Lie $n$-algebroids. |
| title | Brane mechanics and gapped Lie n-algebroids |
| topic | High Energy Physics - Theory Mathematical Physics Differential Geometry |
| url | https://arxiv.org/abs/2404.14126 |