Higgs radial modes and the UV completion of non-linear sigma models

We investigated non-linear sigma models with cosets G/H represented by $SU(N)\times SU(N)/SU(N)$, $SU(N)/SO(N)$, and $SU(2N)/USp(2N)$. These models exhibit a transition to a strongly coupled regime above a threshold energy scale $\Lambda^*$, where the effective field theory approach breaks down. To address this issue, we introduced the so called Higgs radial modes within the Linear Sigma Model, crucial for restoring perturbative unitarity. Analyzing the $N>2$ case, we first notice that all radial modes coming from the most general irreducible representation of G are necessary for unitarizing scattering amplitudes and ensuring the weakly coupled nature of the theory. The phenomenology behind these extra radial modes recalls the physics of the Higgs in the electroweak sector of the Standard Model. In the case of a model describing electroweak symmetry breaking with a more complex pattern, despite strict constraints from electroweak precision tests, these modes could stabilize the Higgs potential and be a possible solution for the vacuum instability issue.