Jacobi Sigma Models

par Janusz Grabowski

vendredi 9 mai 2025, 09:30 → 10:30 Europe/Paris

112 (Bat. Braconnier)

We discuss Jacobi sigma models for general Jacobi structures understood as Jacobi
bundles, i.e., Lie brackets on sections of (possibly nontrivial) line bundles. A particular case
is that of contact manifolds.
The construction is built on a canonical correspondence between Jacobi bundles and homogeneous
Poisson structures on principal bundles with the structure group R^× = GL(1;R).
Consequently, solutions of the field equations are morphisms of certain Jacobi algebroids, i.e.,
principal R^×-bundles equipped additionally with a compatible Lie algebroid structure. Our
sigma models are intrinsically geometric and fully covariant.