2018/09/10 by Hélein, Frédéric, FrÂ\', Frédéric
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1809.03375
For any positive integer n and any Lie group \mathfrakG, given a definite symmetric bilinear form on ℝn and an \hboxAd-invariant scalar product on the Lie algebra of \mathfrakG, we construct a variational problem on fields defined on an arbitrary oriented (n+\hboxdim\mathfrakG)-dimensional manifold Y. We show that, if \mathfrakG is compact and simply connected, any global solution of the Euler--Lagrange equations leads, through a spontaneous symmetry breaking, to identify Y with the total space of a principal bundle over an n-dimensional manifold X. Moreover X is then endowed with a (pseudo-)Riemannian metric and a connection which are solutions of the Einstein--Yang--Mills system of equations with a cosmological constant.