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.
@article{arxiv.1602.00706,
title = {Sigma Models with Negative Curvature},
author = {Rodrigo Alonso and Elizabeth E. Jenkins and Aneesh V. Manohar},
journal= {arXiv preprint arXiv:1602.00706},
year = {2016}
}