Spontaneously broken conformal invariance in observables

TL;DR

The paper shows that spontaneously broken conformal invariance yields a massless dilaton whose soft limit encodes the action of both the dilatation and special conformal generators on observables via Ward identities. It derives explicit relations for massless and massive external legs, demonstrates the role of mass derivatives in the subleading soft limit, and provides concrete applications in Higgs portals, string theory, and D-brane Coulomb branches. At the quantum level, it demonstrates how anomalous dimensions can be incorporated within a conformal regulator to preserve a soft-dilaton identity, with explicit loop examples that support consistency with standard results. The work outlines promising connections to holographic correspondences and cosmology, proposing a framework to explore broken spacetime symmetries across formal and phenomenological settings.

Abstract

Conformal invariance is spontaneously broken in many physical systems leading to the appearance of a single massless Goldstone mode in the spectrum, the dilaton. The dilaton soft limit is shown to generically encode the action of both the dilatation and the special conformal transformation on observables. For massive on-shell legs these take the form of sub-leading soft theorems. At loop level, we show how anomalous dimensions for coupling constants and fields can be included. We illustrate the general analysis with a variety of formal and phenomenological applications.