  In this paper, we present a unified perspective on sphere consistent
truncations based on the classical geometric properties of sphere bundles. The
backbone of our approach is the global angular form for the sphere. A universal
formula for the Kaluza-Klein ansatz of the flux threading the $n$-sphere
captures the full nonabelian isometry group $SO(n+1)$ and scalar deformations
associated to the coset $SL(n+1,\mathbb R)/SO(n+1)$. In all cases, the scalars
enter the ansatz in a shift by an exact form. We find that the latter can be
completely fixed by imposing mild conditions, motivated by supersymmetry, on
the scalar potential arising from dimensional reduction of the higher
dimensional theory. We comment on the role of the global angular form in the
derivation of the topological couplings of the lower-dimensional theory, and on
how this perspective could provide inroads into the study of consistent
truncations with less supersymmetry.

High Energy Physics - Theory