Séminaire de Physique ThéoriqueVector field sigma models, from Lie algebroid Yang-Mills towards nonabelian gerbes
Thomas Strobl (Lyon 1, Institut Camille-Jordan)
Thursday 15 February 2007 14:00 - Tours - Salle 1180 (Bât E2)
Standard sigma models arise by reinterpreting n scalar fields as maps to an R^n equipped with standard flat metric and replacing the latter space by some manifold with geometrical structures such as a Riemannien metric. We reinterpret a Yang-Mills vector field as a vector bundle morphism from the tangent bundle of spacetime to a Lie algebra equipped with a Killing metric. We replace the latter space by a Lie algebroid equipped with a fiber metric generalizing a homogeneous Riemannien manifold to the setting of Lie algebroids. We comment on the physics possibly contained in this novel kind of gauge theories generalizing ordinary Yang-Mills gauge theories. Finally we address the construction of action functionals for nonabelian gerbes and unravel hidden algebroid geometry in that context.