Quantum and classical fields interacting with geometry, Paris

Kaluza-Klein theories without a priori fibration hypotheses

15 avr. 2024, 13:30

1h

amphithéâtre Yvonne Choquet-Bruhat (new building (bâtiment Perrin))

Orateur

Frédéric Hélein (Université Paris Cité, IMJ-PRG)

Description

I will present a theory based on a variational principle, the critical points of which lead to solutions of the Einstein-Yang-Mills equations, in the spirit of Kaluza-Klein theories. The novelty is that the a priori fibration hypothesis is not required: fields are defined on a
"space-time" $Y$ of dimension $4+r$ without a priori principal bundle structure, where $r$ is the dimension of the structure group. If this group is compact and simply connected solutions it allows to construct a 4-dimensional manifold $X$ which can be interpreted as our space-time, in such a way that $Y$ acquires a principal bundle structure over $X$ and produce solutions of the Einstein-Yang-Mills system. If the structure group is $U(1)$ (the case which corresponds to the Einstein-Maxwell system) the situation is slightly degenerated and supplementary hypotheses are necessary.