# The Maximally Symmetric Composite Higgs

## TL;DR

This paper introduces a new class of composite Higgs models based on symmetric coset spaces with maximal symmetry, resulting in a finite, calculable Higgs potential that reduces tuning and improves theoretical consistency.

## Contribution

It proposes the concept of maximal symmetry in composite Higgs models, providing a framework for finite, calculable Higgs potentials and detailed analysis of the SO(5)/SO(4) case.

## Key findings

- Higgs potential becomes finite and fully calculable.
- Maximal symmetry reduces tuning and Higgs mass.
- Detailed analysis of SO(5)/SO(4) model.

## Abstract

We present a novel class of calculable four dimensional composite pseudo-Goldstone boson Higgs models based on symmetric G/H coset spaces which contain a Higgs-parity operator V as well as a linear representation $\Sigma'$ for the Goldstone bosons. For such cosets the low-energy effective Lagrangian for the Standard Model fields can have an enhanced global symmetry which we call the maximal symmetry. We show that such a maximally symmetric case leads to a finite and fully calculable Higgs potential, which also minimizes the tuning by eliminating double tuning and reducing the Higgs mass. We present a detailed analysis of the Maximally Symmetric SO(5)/SO(4) model, and comment on its observational consequences.