  We study a lattice sigma model which is expected to reflect the Anderson
localization and delocalization transition for real symmetric band matrices in
3D. In this statistical mechanics model, the field takes values in a
supermanifold based on the hyperbolic plane. The existence of a diffusive phase
in 3 dimensions was proved for low temperatures. Here we prove localization at
high temperatures for any dimension $d\geq 1$. Our analysis uses Ward
identities coming from internal supersymmetry.
