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

TL;DR

This paper derives new soft theorems at subsubleading order for two types of dilatons, revealing their connection to special conformal transformations and highlighting both similarities and differences.

Contribution

It introduces the first soft theorems at subsubleading order for gravity and Nambu-Goldstone dilatons, linking them to conformal symmetry operators.

Findings

Soft theorems at subsubleading order for gravity dilaton

Soft theorems at subsubleading order for Nambu-Goldstone dilaton

Both theorems involve special conformal transformation operators

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.