Sigma Models with Negative Curvature

TL;DR

This paper constructs a Higgs Effective Field Theory on a hyperbolic scalar manifold with negative curvature, analyzing how curvature affects observable deviations from the Standard Model in particle physics experiments.

Contribution

It introduces a new HEFT framework based on a negatively curved scalar manifold and explores how curvature sign influences experimental signatures.

Findings

The HEFT model has a non-compact O(n,1) symmetry group.

Curvature sign affects deviations in S-parameter measurements.

Cross sections for gauge boson and Higgs scattering depend on manifold curvature.

Abstract

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.