Hidden Conformal Invariance of Scalar Effective Field Theories

TL;DR

This paper reveals that conformal invariance unifies various scalar effective field theories, like Dirac-Born-Infeld and Galileon, by constraining their interactions and amplitudes in specific dimensions.

Contribution

It demonstrates that conformal invariance uniquely determines scalar EFTs related to the double copy and scattering equations, extending their symmetry properties.

Findings

Conformal invariance constrains scalar EFTs to specific interactions.

Amplitudes are fixed by conformal Ward identities.

Theories correspond to specific dimensions, D=0 and D=-2.

Abstract

We argue that conformal invariance is a common thread linking several scalar effective field theories that appear in the double copy and scattering equations. For a derivatively coupled scalar with a quartic ${\cal O}(p^4)$ vertex, classical conformal invariance dictates an infinite tower of additional interactions that coincide exactly with Dirac-Born-Infeld theory analytically continued to spacetime dimension $D=0$. For the case of a quartic ${\cal O}(p^6)$ vertex, classical conformal invariance constrains the theory to be the special Galileon in $D=-2$ dimensions. We also verify the conformal invariance of these theories by showing that their amplitudes are uniquely fixed by the conformal Ward identities. In these theories, conformal invariance is a much more stringent constraint than scale invariance.