Sigma models with negative curvature

We construct Higgs Effective Field Theory (HEFT) based on the scalar manifold HnHn, which is a hyperbolic space of constant negative curvature. The Lagrangian has a non-compact O(n,1)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.