Dilatons Improve (Non)-Goldstones

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 ${\mathcal{L}}_R\propto R{e}^{-2D/F_D}$ 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 $\Delta =d-2$.

Comments: 20 pages + refs, 1 figure, major revision. Includes discussion on Weyl-gauging and the effect of the improvement on gravitational form factors