  We construct Higgs Effective Field Theory (HEFT) based on the scalar manifold
H^n, which is a hyperbolic space of constant negative curvature. The Lagrangian
has a non-compact O(n,1) global symmetry group, but it gives a unitary theory
as long as only a compact subgroup of the global symmetry is gauged. Whether
the HEFT manifold has positive or negative curvature can be tested by measuring
the S-parameter, and the cross sections for longitudinal gauge boson and Higgs
boson scattering, since the curvature (including its sign) determines
deviations from Standard Model values.
