Gauged diffeomorphisms and hidden symmetries in Kaluza–Klein theories

Abstract

We analyse the symmetries that are realized on the massive Kaluza–Klein modes in generic D-dimensional backgrounds with three non-compact directions. For this, we construct the unbroken phase given by the decompactification limit, in which the higher Kaluza–Klein modes are massless. The latter admits an infinite-dimensional extension of the three-dimensional diffeomorphism group as local symmetry and, moreover, a current algebra associated with together with the diffeomorphism algebra of the internal manifold as global symmetries. It is shown that the ‘broken phase’ can be reconstructed by gauging a certain subgroup of the global symmetries. This deforms the three-dimensional diffeomorphisms to a gauged version, and it is shown that they can be governed by a Chern–Simons theory, which unifies the spin-2 modes with the Kaluza–Klein vectors. This provides a reformulation of D-dimensional Einstein gravity, in which the physical degrees of freedom are described by the scalars of a gauged nonlinear σ-model based on , while the metric appears in a purely topological Chern–Simons form.