Jacobi algebroids and Jacobi sigma models
Fabio Di Cosmo, Katarzyna Grabowska, Janusz Grabowski

TL;DR
This paper generalizes Jacobi sigma models to Jacobi bundles, introducing a homogeneity structure and Jacobi algebroids, and explores their solutions, extending to almost Poisson and Jacobi brackets in a geometric, covariant framework.
Contribution
It introduces a unified approach to Jacobi sigma models on Jacobi bundles using homogeneity structures and Jacobi algebroids, extending to non-Jacobi brackets.
Findings
One-to-one correspondence between different models' solutions.
Extension to almost Poisson and Jacobi brackets.
Geometric and fully covariant sigma models.
Abstract
The definition of an action functional for the Jacobi sigma models, known for Jacobi brackets of functions, is generalized to \emph{Jacobi bundles}, i.e., Lie brackets on sections of (possibly nontrivial) line bundles, with the particular case of contact manifolds. Different approaches are proposed, but all of them share a common feature: the presence of a \emph{homogeneity structure} appearing as a principal action of the Lie group . Consequently, solutions of the equations of motions are morphisms of certain \emph{Jacobi algebroids}, i.e., principal -bundles equipped additionally with a compatible Lie algebroid structure. Despite the different approaches we propose, there is a one-to-one correspondence between the space of solutions of the different models. The definition can be immediately extended to \emph{almost…
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models
