Hidden Conformal Invariance of Scalar Effective Field Theories

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 $\mathcal{O}(p^4)$ 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 $\mathcal{O}(p^6)$ 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.

7 pages

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• The ChPT: top-down and bottom-up
• FiniteFieldSolve: Exactly Solving Large Linear Systems in High-Energy Theory
• Next-to-MHV Yang-Mills kinematic algebra
• On the Conformal Symmetry of Exceptional Scalar Theories