Symmetry and Unification from Soft Theorems and Unitarity

TL;DR

This paper demonstrates that symmetry and unification naturally emerge at high energies in scalar field theories under unitarity and Adler zero conditions, linking scattering constraints to fundamental symmetries.

Contribution

It provides a proof that physical constraints like unitarity and Adler zero lead to unification into symmetry multiplets in a broad class of scalar theories.

Findings

High-energy unification into symmetry multiplets

Explicit derivation of symmetry generators from spectrum

Coset space is shown to be symmetric

Abstract

We argue that symmetry and unification can emerge as byproducts of certain physical constraints on dynamical scattering. To accomplish this we parameterize a general Lorentz invariant, four-dimensional theory of massless and massive scalar fields coupled via arbitrary local interactions. Assuming perturbative unitarity and an Adler zero condition, we prove that any finite spectrum of massless and massive modes will necessarily unify at high energies into multiplets of a linearized symmetry. Certain generators of the symmetry algebra can be derived explicitly in terms of the spectrum and three-particle interactions. Furthermore, our assumptions imply that the coset space is symmetric.