Brane mechanics and gapped Lie n-algebroids

Athanasios Chatzistavrakidis; Toni Kodžoman; Zoran Škoda

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arXiv · 2404.14126

Brane mechanics and gapped Lie n-algebroids

Athanasios Chatzistavrakidis·Toni Kodžoman·Zoran Škoda

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Abstract

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.

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Athanasios Chatzistavrakidis, Toni Kodžoman, Zoran Škoda. 2024-04-22. Brane mechanics and gapped Lie n-algebroids. https://arxiv.org/abs/2404.14126

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