Dilatons Improve (Non)-Goldstones

TL;DR

This paper explores how dilatons, as Goldstone bosons of spontaneously broken conformal symmetry, can be conformally coupled through an improvement term, affecting gravitational form factors and revealing insights into chiral symmetry breaking.

Contribution

It demonstrates the role of an improvement term in conformally coupling dilatons and other particles, impacting gravitational form factors and providing new insights into spontaneous chiral symmetry breaking.

Findings

Improvement term enables conformal coupling of dilatons to other particles.

Gravitational form factors exhibit a dilaton pole in the spin-zero channel.

Operator driving chiral symmetry breaking has scaling dimension Δ = d - 2.

Abstract

Shift symmetry forbids conformal coupling of Goldstone bosons from internal symmetries, but not for spontaneously broken conformal symmetry. Its Goldstone boson, the dilaton $D$, admits and indeed requires, an improvement term $ {\cal L}_R \propto R e^{-2D/F_D}$ as it realises the Goldstone matrix element in the effective theory. The improvement, combined with Weyl-gauging, enables conformal coupling to Goldstone bosons and other particles of arbitrary Weyl-weight. While improvement does not affect scattering amplitudes in flat space, it impacts gravitational form factors decisively, giving rise to the dilaton pole in the spin-zero channel. We compute leading-order scalar, fermion, pion, and dilaton form factors, confirming low-energy constraints. The dilaton decoupling limit further implies that the operator driving spontaneous chiral symmetry breaking has scaling dimension $\Delta= d-2$.