Dynamical mechanisms for Kaluza-Klein theories

Mécanismes dynamiques pour les théories de Kaluza-Klein

Frédéric Hélein (1)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

We present variational formulations of gauge theories and Einstein-Yang-Mills equations in the spirit of Kaluza-Klein theories. For gauge theories only a topological fibration is assumed. For gravitation coupled with gauge fields no fibration is assumed: fields are defined on a 'space-time' Y of dimension 4 + r without any structure a priori, where r is the dimension of the structure group. If the latter is compact and simply connected, classical solutions allow to construct a manifold X of dimension 4 to be the physical space-time, in such a way that Y acquires the structure of a principal bundle over X , and lead to solutions of the Einstein-Yang-Mills systems.

Domaines: Physique mathématique [math-ph]; Physique des Hautes Energies - Théorie [hep-th]; Géométrie différentielle [math.DG]

Frédéric Hélein. Dynamical mechanisms for Kaluza-Klein theories. 2022. ⟨hal-03513721v2⟩