New soft theorems for the gravity dilaton and the Nambu-Goldstone dilaton at subsubleading order

TL;DR

The paper establishes that two distinct dilaton species—the gravity dilaton and the NG dilaton—exhibit soft theorems fixed through subsubleading order $\mathcal{O}(q^{1})$. For the gravity dilaton, gauge invariance alone determines the soft behavior at this order, while for the NG dilaton, Ward identities of scale and special conformal transformations fully fix the corresponding soft expansion; in both cases the soft amplitude is expressible in terms of lower-point amplitudes via conformal generators $\hat{\mathcal{D}}$ and $\hat{\mathcal{K}}_\mu$. The results highlight deep structural parallels between gravitational and conformal symmetries in determining low-energy dilaton dynamics, and clarify differences arising from string versus field-theory limits, with implications for loop corrections and anomalies.

Abstract

We study the soft behavior of two seemingly different particles that are both referred to as dilatons in the literature, namely the one that appears in theories of gravity and in string theory and the Nambu-Goldstone boson of spontaneously broken conformal invariance. Our primary result is the discovery of a soft theorem at subsubleading order for each dilaton, which in both cases contains the operator of special conformal transformations. Interesting similarities as well as differences between the dilaton soft theorems are discussed.